1. Introduction

During the past few years, substantial research efforts were focused on slow light structures and their applications. It has been shown that when light propagates through coupled cavity waveguides (CCWs) a significant reduction of its group velocity is achieved. Since CCWs can be realized in chip-scales, the slowing effect opens up new avenues for numerous integrated optics applications e.g. delay lines, rotation sensors, optical memories, optical filters, wavelength converters and more [1–7].

Considerable reduction of the group velocity requires weak coupling between adjacent cavities causing the light to circulate in the cavities for long periods. However, losses in the individual cavities may reduce the intensity of the propagating signal, thus necessitating high quality factor (Q) cavities. While it is possible to fabricate and couple very high Q resonators (see e.g [8].), the fabrication complexity, high cost and low yield of such processes render them less appropriate for commercial optical devices. As an attractive alternative to such passive high Q structures, the employment of coupled active cavities, such as semiconductor lasers (in particular, vertical cavity surface emitting lasers - VCSELs) has been suggested [9]. The advantages of this approach are twofold. First, the gain in the individual cavities can compensate for the optical losses. Second, the control over the pumping level in each cavity provides an additional degree of freedom which allows one to dynamically modify the properties of structure and manipulate light pulses, thus enabling several interesting applications, e.g., optical buffers, all-optical switches/routers and all-optical regenerators [10]. In particular, by turning off the pump in a single cavity it is possible to block the propagation of an optical pulse and to direct it to a desired route. Pulse stopping utilized by dynamically tuning the loss and resonance frequencies of coupled cavities have been proposed [5,11]. In [5] the loss of every second cavity was increased to decouple the adjacent cavities while in [11] the resonance frequencies where tuned to achieve the decoupling effect.

In this paper, we propose and analyze a dynamically controlled semiconductor laser array as a slow-light waveguide for telecommunications. Our scheme is based on capturing the pulse information (“0” or “1”) by using its power to seed lasing in a single cavity. The shape of the retrieved pulse is found to be determined solely by the retrieval mechanism, thus providing a powerful tool for compensating all types of distortions (as will be discussed in section 3). Diverse applications such as optical buffers, routers and synchronizers are presented and studied. In section 2 we present the theoretical framework used for our simulations; in section 3 we study conventional, straightforward, trap and release process and present its inherent problems, we also present and study pulse trapping and releasing using the seeding concept. In section 4 we discuss the results and summarize. Previous work was presented in [10], this paper expand s on it and develops and elaborates on the seeding process.

2. Theoretical framework

The dynamics of coupled lasers array is described by the rate equations [9, 10, 12, 13] –

 

Fig. 1 Pulse reflection caused by change of pump in laser #350 (Media 1).

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The array consists of 500 elements with normalized coupling coefficient η = 0.01, p = 0 in the lasers on the left of the reflection point (laser #350) in which p = 10⁻². The pulses are injected into the array with coupling efficiency η_ext = 0.03, and normalized pulse intensity of 5·10⁻⁴.

3. Pulse storage and release

As was shown in [10], optical pulses can be injected into the array and removed from it fairly easily. However, the maintaining of the pulse within the array is more difficult. As can be seen from (2), the dispersion around resonance is relatively constant, resulting in a steady broadening of the signal. Consequently, one cannot store a pulse in the array for long periods.

3.1 Pulse Trapping

A relatively simple approach for trapping a pulse in the array is deactivating the lasers from both sides of it, thus effectively “trapping” it in a smaller array. As long as these lasers are deactivated, the pulse propagates back and forth between them, without leaking power into the rest of the array. It is also possible to move the trap by adiabatically by sequentially activating and deactivating the lasers in the direction in which we wish to lead the pulse. The trapping of a pulse and the movement of the trap are shown in Fig. 2 below.

 

Fig. 2 Multi-cell trap. (a) An optical pulse is inserted into the array. (b) Pulse is reflected from right boundary (c) Trap size is gradually decreased, leading to stable optical power in the trap. (d) Trap is moved forward.

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As long as the optical pulse is contained in the trap its width is determined by the trap size and its power can be controlled by changing the pump parameter in the trap area, thus enabling the conservation of an optical bit for an arbitrarily long period of time. With this method, several pulses can be inserted and stored in the array for arbitrary long periods of time with no crosstalk between them. The capacity of the array is - C = N_lasers/(S_trap + S_deac), where N_lasers is the number of lasers, S_trap and S_deac are respectively the number of lasers comprising the trap and the deactivated parts. Detailed studies of this process show that the pulse is well contained within the trap if the number of deactivated lasers is larger than two (from both sides).

Although the power of the injected pulse is preserved it is unable to preserve the pulse shape. Although the trapped pulse does not broaden, it does fold onto itself each time it is reflected from one of the deactivated lasers, and therefore continues to accumulate phase in the same manner as a propagating pulse. As a result, when released from the trap, the pulse quickly disintegrates, as shown in Fig. 3 and in the attached multimedia file, and is unusable for further processing.

 

Fig. 3 The result of releasing a pulse from a multi-cell trap. Pulse release is accomplished by re-activating the lasers in front of the trap. (a) Optical energy is trapped (b) front block of the trap is removed, allowing pulse to propagate (c) Shortly after release, accumulated phase causes the pulse to evenly spread over the entire array. (Media 2)

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3.2 Trap seeding

As an alternative approach, we propose to trap the pulse using a single laser in the array. Effectively, such a trap conforms to the equations governing a single laser, and a pulse trapped in it loses its phase information relative to its neighboring lasers. Releasing a pulse from this trap is equivalent to coupling a single laser to an array of similar optical resonators, or to a fiber, and its output is determined by the process employed for its extraction. The seed and release process consists of the following steps - (1) Trapping the incident pulse by deactivating all lasers in which it is exists except one. (2) Regenerating the lost power by increasing the pump parameter in that laser. (3) Releasing the pulse by adiabatically reactivating the lasers in front of the trap (or behind it). The release mechanism determines the shape of the output pulse. A slow, adiabatic pulse release from the trap generates a powerful but broad pulse while a faster release creates a less energetic (but shorter) Gaussian pulse.

Figure 4 illustrates this process for two scenarios - trapping a regular (transform-limited) Gaussian pulse (4ns width, power of 1.2*10⁻⁴ in AU, marked in red), and trapping a dispersed one (same as red pulse, chirped to 10ns - blue). As shown in the figure, despite the differences in the captured pulses, the released pulses are identical. It should be emphasized that the two scenarios were not conducted simultaneously and that the plots in Fig. 4 are simply overlaid. The multimedia file shows the dynamics of the trap & release process. It is also important to note that because the properties of output pulse are independent of those of the input pulse due to loss of phase, the trap also perform a regeneration process.

 

Fig. 4 - Trapping and release of optical pulses from a single cell trap. Red - normal pulse (trapped at laser #300 in the array), blue - dispersed pulse (trapped at laser #260). (a) Optical pulses inserted into array. (b) Pulses are trapped in single cell. (c) Trapped pulses. (d) Release from trap (e) continued propagation. (Media 3)

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The seeding process is directed as follows– (a) Deactivation of 50 lasers around the trap (to the value of p = −1e⁻²). (b) Gradual increase of the pump inside the trap, to p = 2.1e⁻³. (c) Gradual decrease of the pump power inside the trap cell to p = 2e⁻³(pump value is relatively unimportant for times <10μs). Release of pulse from the trap is performed adiabatically. First, the array is reactivated except for three lasers in front of the trap cell and five behind it. The trap cells are then reactivated sequentially, from the farthest one from the laser to the adjacent one. Because of there are more deactivated lasers behind the trap than there are in front of it, the optical power is coupled forward resulting in a forward propagating Gaussian pulse.

The same process can be performed with no incident optical power (i.e. a “0” bit). In this case there is no power trapped in the trap laser and the release process does not generate an output pulse. Therefore, the seeding process can trap a bit and reconstruct it regardless its logical value, essentially creating an optical memory. Figure 5 shows the power build up in the trap laser when trapping a “1” bit (blue) and a “0” bit (red). A “0” bit does not generate power build up in the trap while a “1” bit does. Thus it is possible to regenerate the original characteristics of an incident pulse (essentially, its logical value), serving as optical memory.

 

Fig. 5 - A comparison between the optical power in a seeded (blue) and an “empty” trap (red) as a function of time.

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A logical “0” means that when no input is entered into the laser trap, no optical power will be released. By carefully choosing the value of p, the noise buildup in the trap is controlled and the memory can be maintained for long periods of time (>50μs has been observed).

By modifying the release mechanism, one can control the properties of the regenerated pulse such as its propagation direction, duration, etc. This property gives rise to a possible additional application of the seeding process for rate conversion in telecommunication applications. In the telecommunications industry there is considerable effort in research and development of all-optical networks, in which signals remain in the optical domain throughout their routing [15]. One of the basic building blocks considered for such a network is a rate converter which allows the up-conversion of several slow bit streams into one faster stream, or the down-conversion of a single fast bit stream into several slower ones. For example, it may be necessary to convert four NRZ-STM16 2.5GBps data streams from a local network into a single NRZ-STM64 10GBps stream which is then transmitted over a backbone channel.

Consider four low-rate communication-lines which should be multiplexed into a single, faster, channel. Such conversion may be accomplished all-optically by the following steps: (a) The four incoming bit streams seed the laser trap in four distinct delay lines. (b) Each released bit is “squeezed” according to the necessary ratio. (c) The timings of the release processes from each the four lines are set so that their output matches a distinct time slot, resulting in a multiplexed, faster bit stream. (d) The combined bit stream is amplified to compensate for the losses incurred in the conversion. Similarly, it is possible down-convert a stream (de-multiplexing). The fast bit-stream is split into several distinct delay lines where in each delay-line the bit is trapped and released to form a longer pulse.

4. Discussion and summary

We studied the dynamics of optical pulse propagation through a slow-light structure comprised of active cavities. By controlling the pump parameter in laser array it is possible to trap, store and regenerate optical pulse traveling through the array. The key ingredient is the ability to electrically change the pump level in individual cavity, enabling versatile control over the properties of the array. Active control over the gain and loss in the cavities provides a powerful mechanism to route, eliminate and enhance (regenerate) optical information without necessitating detection and electrical recreation of the optical information.

The proposed scheme can be realized using a coupled semiconductor laser arrays, in particular a VCSEL array [10]. To realize a structure such as the one simulated here coupled mode theory was used to determine the size of the individual VCSELs, the gap between them and the required refractive index. Assuming a refractive index of n = 3.55 in the core of a VCSEL, and requiring that each VCSEL be a single mode structure, the time required for the optical power to move between two adjacent VCSELs (coupling time) for different radii can be computed. Thus for a VCSEL with a diameter of 2μm, an approximate gap of 2.4μm between two adjacent ones with a surrounding refractive index of n = 3.5 will allow a coupling time of 200ps. Fabrication of smaller VCSELs permits higher index contrast, but requires smaller gaps between the neighboring cavities. For a VCSEL with a radius of 1μm surrounded by a refractive index of n = 3.35, the mode is compressed leading to a gap distance of 1.5μm.

This tradeoff between the gap distance and the refractive index has interesting implications for future fabrication of such structures but is beyond of the scope of this paper. Although the array studied here was composed of 500 VCSELs, its circular geometry, allows for smaller arrays which can simplify the fabrication process. For example, arrays of 224 VCSELs have been demonstrated experimentally [16].Although this study focused on optical memory, the proposed concept can facilitate the realization of additional applications such as pulse synchronization, optical routing, switching, and bit-rate conversion.