We show that a photonic transistor device can be realized via the manipulation of optical interference by optically controlled gain or absorption in novel ways, resulting in efficient transistor signal gain and switching action. Exemplary devices illustrate two complementary device types with high operating speed, µm size, µW switching power, and switching gain. They can act in tandem to provide a wide variety of operations including wavelength conversion, pulse regeneration, and logical operations. These devices could have a Transistor Figure-of-Merits >105 times higher than current χ(3) approaches and are highly attractive.
©2008 Optical Society of America
To further increase the speed of optical networks, there are substantial interests in exploring the use of all-optical devices to realize 10–100Gbit/s all-optical switching. Beside their high speed, all-optical devices could help to substantially reduce the power consumption of current optical network equipments involving optical-electrical-optical (OEO) conversions . The realization of photonic transistors capable of all-optical signal processing such as switching, signal amplification, logical operations, wavelength conversion, and pulse regeneration is of great interest .
The all-optical devices of interest for high-speed networks include all-optical wavelength converters, all-optical switches, and all-optical logic gates. These all-optical devices will also enable ultrafast all-optical signal processing and computing. However, the reason why all-optical devices have not yet seen large insertion in practice is because they are still marginal in performance for the desired device properties.
While ultrafast all-optical operations can be realized using materials with third-order optical nonlinearity χ (3) (or nonlinear refractive index n (2)), the lack of materials with high enough χ (3) gives rise to the requirement of needing either very high optical intensity (~1010 W/cm2), long device length (~ km), or narrowband high-Q cavity to compensate the low χ (3) . The desire for integration makes it even more demanding as it further restricts the class of materials suitable. For example, III–V semiconductors such as GaAs at below half the bandgap energy are suitable for integration and have comparatively high n (2), but as shown experimentally [3,4], a 1cm-long device still needs switching peak power of ~10W for the control beam even with the use of a strongly confined waveguide with <0.5µm2 mode area (at λ=1550 nm). While the use of a nano-waveguide similar to that in a photonic-wire laser  could reduce the mode area to 0.04 µm2 or switching power to ~1W, it would still be 100× higher than the ~10 mW power available from typical semiconductor lasers. The use of χ (2) media such as PPLN utilizing parametric gain to realize wavelength conversions or switching like behaviors also results in devices that are a few centimeters in length and requiring beam powers of ~1W . Recently, there has also been interest in using the higher though slower n (2) of semiconductor optical amplifiers (SOAs) for 10–100 Gb/s operations, resulting in millimeter-size devices [7–9]. However, similar problems remain, as each SOA pair requires high electrical power (~0.5W) and careful biasing to operate.
An all-optical switch with switching gain is often referred to as photonic transistor. Beside the problems mentioned above, switching gain is another challenge for current all-optical switches. In this paper, we will describe a new approach to realize high-speed all-optical switches with switching gain that could be much smaller in size and with substantially lower power consumption than current approaches, resulting in novel photonic transistor devices that are highly efficient. In section 2, we first review how an all-optical switch with switching gain could be seen as the photonic analog of electronic transistor. In Section 3, we will describe problems in current approaches. In section 4, we introduce our approach and describe its motivation. We then discuss an analytical analysis showing the basic principles governing the device operations. In section 5, we discuss the all-optical operation of our photonic transistor devices in detail. We first describe the basic operational principles for the two complementary types of photonic transistors that can perform wavelength down conversion and wavelength up conversion. They are referred to as energy-up photonic transistor (EUPT) and energy-down photonic transistor (EDPT), respectively, where up or down refers to the conversion being upward or downward in energy. In section 6, we describe in detail the simulation of the photonic transistor in high-speed operation using computational electromagnetics based on a Finite Difference Time Domain (FDTD) method that incorporates full medium dynamics. We discuss how the EDPT and EUPT can be cascaded together to form a “full photonic transistor” capable of a wide variety of operations including signal gain, logical operations, and both energy up and energy down conversions. In section 7, we discuss a photonic-transistor figure-of-merit (PT-FOM) factor that takes into account the key desirable properties of a photonic transistor, including its size, power consumption, speed, optical bandwidth, and gain. The PT-FOM will allow us to rate various types of all-optical transistor devices with respect to each other and with respect to electronic transistors. This is then followed by the summary.
2. Photonic transistor as photonic analog of electronic transistor
All optical switching devices are often compared to electronic transistors. The case of a commonly used n (2) based switch with Mach Zehnder Interferometer (MZI) geometry is shown in Fig. 1(a) in which a strong control pulse is sent into the top arm of the MZI, causing a π phase shift in the top arm. A weak signal pulse traveling concurrently through the MZI will exit Port A if the control pulse is absent and Port B if the control pulse is present. Let us call this to be the “optical switching configuration”. This MZI all-optical switch can function in another configuration that is often used for wavelength conversion as shown in Fig. 1(b). In the wavelength converter configuration, the “signal beam” is a continuous-wave (CW) laser beam at wavelength λ1. The “control beam” is where one sends in an input pulse at wavelength λ2 that may be different from λ1. The input pulse at λ2 then generates an output pulse at λ1 exiting Port B, essentially by switching the CW beam at λ1 from Port A to Port B.
This “wavelength conversion configuration” is most easily compared to an electronic transistor by re-labeling the CW beam as “power supply beam” and the input pulse as the “input signal beam”. In that case, the device shown in Fig. 1(b) can be represented as the functional black box shown in Fig. 2(a) illustrating an input signal beam switching a CW power supply to generate an output signal beam. In principle, with a strong CW power supply beam, the output signal beam could have higher power than the input signal beam, resulted in “switching gain”, or power amplification. It is noted as “in principle” as in practice, there are various problems encountered by n (2) or χ (3) based devices as discussed in Section 3. The “amplified power” is supplied by the CW power supply beam.
For comparison, Fig. 2(b) shows the case of an electronic transistor such as a Field Effect Transistor (FET) for which an input signal voltage applied to the Gate terminal (G) modulates the amount of current exiting the Drain terminal (D) when a Power Supply source is connected to the Source terminal (S). This current modulation is achieved by modulating the “electrical resistance” of the narrow electrical channel connecting the Source terminal to the Drain terminal. Note that the word “transistor’ comes from “transfer resistor”. The analogy is even more complete when compared to a bi-polar transistor that acts more directly as a current amplifier (current as made up of flow of electrons can be seen as equivalent to optical beam as flow of photons).
From the above discussion, we may say that an all-optical switch with switching gain for which the output signal power is more than the input signal power can be referred to as “Photonic Transistor”, just like an electronic transistor is capable of output signal power gain.
3. Problems with current approaches
While most of the current approaches focused on realizing all-optical switch using χ (3) or n (2) materials, beside the power-consumption and size problems mentioned above, there are two other problems. First, non-square pulses will experience frequency chirping because the nonlinear phase shift induced will vary with the pulse intensity profile, resulting in spectral broadening under self- or cross- phase modulation (see Section 6.5) . Second, while it is desirable to achieve switching gain so that a weak control beam can switch a strong signal beam, in practice when the control beam induces π phase shift, the much stronger signal beam will experience self-phase modulation of multiple π, resulting in serious spectral broadening as well as encountering multi-photon absorption . These problems make the devices not very cascadable, which is essential for complex photonic circuits. As elaborated above, achieving switching gain is an important criterion that qualifies an all-optical device to be a “photonic transistor” instead of just a lossy all-optical switch.
Another approach in realizing all-optical devices made use of material gain or absorption to realize switching. In principle, the use of gain or absorption can make the device operate with significantly lower power as they involve lower-order nonlinearity as compared with the use of χ (3) medium that is third order nonlinearity. Higher-order nonlinearity is intrinsically weak, resulting in much higher power requirement. However, current all-optical devices based on material gain or absorption suffer from low operating speed and the lack of switching gain. The reason is illustrated in Fig. 3.
For the purpose of illustration, to understand these problems, Fig. 3(a) shows a simple all-optical switch based on active medium capable of gain or absorption. It is made up of two crossing waveguides with an active medium at the cross-section of the two waveguides (a more realistic device could involve, for example, two counter propagating beams thorough a single waveguide but the physics will be the same). Power supply beam IPS with intensity below the saturation intensity of the medium entering from the top will not be able to pass through the medium because of absorption. An input signal beam IS with intensity higher than the saturation intensity of the active medium (ISAT) is used to excite the active medium and allow the power supply beam IPS to pass through the medium and generate an output signal beam ISOUT. One main problem for such switch based on active medium is that although the turn-on process can be fast by saturating the medium using a strong input signal beam IS with intensity higher than ISAT, the turn off process is slow when the input signal beam is off. The medium will recover with spontaneous decay time typically on the order of nanosecond for semiconductors. A second main problem is that the power supply beam IPS must have lower power then the input signal beam IS or it will saturate the medium by itself and self switched through even before the input signal pulse enters (i.e. IPS<IS, see Fig. 3(b)). As a result, the device cannot have switching gain. This is because the output signal power ISOUT has to be smaller than the power supply power (i.e. ISOUT<IPS) and hence the output signal power has to be smaller than the input signal power (i.e ISOUT<IS) if IPS<IS.
4. Introduction to our approach
To circumvent the above limitations while still keeping the low power advantage of gain and absorption, we propose a new all-optical switching device scheme utilizing the modulation of optical interference by medium gain and absorption. We will refer to this new scheme as Gain or Absorption Manipulation of Optical Interference (GAMOI). In this paper, we will show how to use GAMOI to realize various highly efficient photonic transistor devices. To the best of the authors’ knowledge, this is the first detailed investigation on how to use absorption and gain to affect optical interference for realizing all-optical photonic transistor devices. As will be shown in detail later, this new scheme can achieve highly efficient and high speed photonic transistor actions. The main innovation in our approach can be summarized as follows.
Firstly, optical interference structure is used in combination with the active medium gain and absorption change. The interference structure prevents the power-supply beam from self switching even when the intensity of the power-supply beam is much higher than the saturation intensity of the medium, which is needed to achieve switching gain.
Secondly, two different wavelengths are used for the power-supply beam and the input signal beam. This enables the use of saturation or stimulated emission in the turning on or off phase of the switching action, resulting in fast switching operations, thereby evading the device speed limitation imposed by slow carrier decay.
Finally, because it is necessary to use optical beams at two different wavelengths, we propose two complementary photonic transistor structures to achieve both wavelength up-conversion and down-conversion. Having wavelength up and down conversion capability is essential in all-optical circuits, as one main advantage of an all-optical system comparing to an electronic system is its huge bandwidth capability. However, to fully utilize the advantage of optical bandwidth, the system should be able to work with multiple signal wavelengths, and capable of wavelength conversion between different operating wavelengths when necessary. Thus, the inherent wavelength conversion capability of the photonic transistor devices we proposed here is highly desirable.
We illustrate the new approach here using the case of an optical-interference based directional coupler, in the form of two coupled waveguides, as the interference device. However, the readers should keep in mind that couplers are not the only choice available to introduce the optical interference. Various other structures, such as multi-mode waveguide interferometers and resonators, can also be used. Here we focus on the case of the directional coupler, because of its familiarity for most researchers in the field, and that it is relatively easy to analyze.
4.1 Directional couplers with absorption and gain
The directional coupler is an interesting device that has been studied quite extensively over the past several decades . The most basic form of a directional coupler is two identical waveguides laid in parallel to each other, and separated by a certain distance. The optical field entering one waveguide will be coupled to the other waveguide, and vice versa. As a result, the optical power will be exchanged between the two waveguides periodically. The length over which the power is completely exchanged from one waveguide to another is referred to as one full coupling length.
The most basic form of a directional coupler is when the two waveguides are identical and transparent. It is commonly known that when the two waveguides are non-identical in propagating refractive index, the power exchange between the two waveguides can no longer be complete. A less commonly known fact is that gain and absorption in one or both of the waveguides will also drastically change the coupling characteristics. As a result, if either the refractive index or the gain/absorption coefficient of the coupler can be modified in some way, the coupler can act as an optical switching device.
Even though much research efforts have been done on utilizing the directional coupler as optical switching devices , most research focused on utilizing the change in the refractive index in the coupler (e.g. through nonlinear refractive index n (2)) to achieve optical beam switching. Here, we focused on utilizing optically controlled gain and absorption to affect the optical interference, resulting in novel all-optical switching actions.
In the directional coupler implementation of our device, the device geometry of interest will involve two coupled waveguides but is unusual in that certain part of the waveguides is not transparent but is filled with active medium capable of gain or absorption. In quasi-static or DC operation, the gain or absorption manipulation of optical interference (GAMOI) principle we use in such a directional coupler device can be treated by extending the typical coupled mode theory as follows.
Consider two waveguides (WG1 and WG2) in close proximity to each other such that the evanescent field from one waveguide may be coupled to the other waveguide and vice versa. Let a 1 be the instantaneous field amplitude in WG1 and a 2 be the instantaneous field amplitude in WG2. The field amplitudes are defined here in terms of power (e.g. the power flow in WG1 is given by P 1=|a 1|2). We assume that WG2 has a lossy medium with field absorption coefficient α. Constants k 12 and k 21 are the coupling coefficients describing the rate that power is transferred from WG1 to WG2 and vice versa. If the full coupling length is LC and the waveguide is transparent so α=0, then k 12=k 21=π/(2LC). β1 and β2 are the complex field propagation k-vector constants for WG1 and WG2, respectively.
Let us define γ2=(π/2LC)2-α2/4. The power exchange between the two waveguides when a unit power is launched into WG1 at position z=0 so a 1(0)=1 and a 2(0)=0, can be calculated as follows :
When γ2>0, power exiting at length z is:
When γ2<0, power exiting at length z is:
From these equations, we can see that change in the absorption or gain coefficient in the coupler could lead to large change in the two output ports of the coupler. This is the basic principle behind our photonic transistor devices.
4.2 Absorption manipulation of optical interference (AMOI)
One type of device geometry of interest is shown in Fig. 4(a), which uses absorption manipulation of optical interference (AMOI). The length of the coupler is chosen so when the top waveguide is transparent, the total length is the whole coupling length LC so all the light entering from the bottom waveguide will exit the top waveguide (Fig. 4(b)). When the top waveguide becomes absorptive, part of the light will exit the bottom waveguide (Fig. 4(c)).
We vary the absorption coefficient α of the top waveguide and plot the output powers from PS-OUT and SIG-OUT (PPS-OUT and PSIG-OUT) as a function of αLC in Fig. 5. The normalized output powers are dependent only on the product αLC and are independent on the individual values of α and LC.
From Fig. 5, we see that when αLC=0, we have PPS-OUT=PPS-IN and PSIG-OUT=0 since the input beam entering the bottom transparent waveguide will be coupled to the top waveguide completely when the top waveguide is transparent with α=0 (Fig. 4 (b)). When αLC increases from 0 to 5 so that the top waveguide becomes absorptive, PSIG-OUT increases while PPS-OUT decreases, and the total output decreases as a result of the absorption. When αLC increases to 50, PSIG-OUT reaches 80% of the input power and significant amount of the power-supply power has been switched out from the bottom waveguide (Fig. 4(c)). At this point, the system actually sees little total loss as shown by the upper line in Fig. 5 labeled as PSIG-OUT+PPS-OUT. This is because at high absorption, the small energy leakage to the top waveguide has no chance to build up constructively, resulting in little energy transfer to the top waveguide and hence little absorption. This “high-absorption induced switching” phenomenon also occurs in the case of metallic mirror in which the highly absorptive metal actually causes impinging light beam to strongly reflect back.
We can also obtain the results of Fig. 5 using FDTD numerical simulation method. The results of the FDTD simulation are also shown in Fig. 5 as discrete data points, which agree well with those obtained by the analytical equations.
4.3 Gain manipulation of optical interference (GMOI)
Another type of geometry of interest is shown in Fig. 6(a), which used the gain coefficient change in part of the coupler to modify the output and is referred to as Gain Manipulation of Optical Interference (GMOI). The length of the coupler is also chosen so when the top waveguide is transparent, the total length is the whole coupling length LC so all the light entering from the top waveguide will exit the bottom waveguide (Fig. 6(b)). When the right half of the top waveguide becomes amplifying, part of the light will exit the top waveguide (Fig. 6(c)).
We vary the gain coefficient -α (negative alpha is gain coefficient) of the active section and plot in Fig. 7 the output powers from PS-OUT and SIG-OUT (PPS-OUT and PSIG-OUT) as a function of -αLC. Again, the normalized output powers are dependent only on the product αLC and are independent on the individual values of α and LC.
From Fig. 7, we see that when α=0 so that -αLC=0, we have PPS-OUT=PPS-IN and PSIG-OUT=0. When -αLC (α<0 indicates gain) increases as the gain goes higher, PSIG-OUT will increase faster than PPS-OUT. After -αLC reaches 7, PSIG-OUT is actually higher than PPS-OUT and significant amount of the power-supply power has been switched out, which is a good point to operate. This “gain-induced switching” phenomena also occurs in the case of optical amplifier in which gain can cause “gain guiding” even in the absence of refractive index guiding.
We can also obtain the results of Fig. 7 using FDTD numerical simulation method. The results are also shown in Fig. 7. as discrete data points, which agree well with those obtained by the analytical equations.
In the following sections, we will discuss how to use the gain and absorption manipulation of optical interference to realize all-optically operated energy up photonic transistor and energy down photonic transistor. Note that for all the discussion below, we assume the using of direct bandgap semiconductor material to provide the gain and absorption so that we can realistically evaluate a practical implementation of the devices.
5. All-optical operation of the photonic transistors
5.1 The energy-up photonic transistor (EUPT)
First, let us describe the all-optical operation of the energy-up photonic transistor (EUPT). The structure of EUPT is shown in Fig. 8. The device has various input/output ports labeled as PS-IN (power-supply in), SIG-IN/PS-OUT (signal in/power-supply out), and SIG-OUT (signal out). Two optical inputs are involved in the operation and their wavelength is labeled as λH and λL, while λH refers to the input with higher photon energy or shorter wavelength, and λL refers to the input with lower photon energy or longer wavelength (i.e. the subscript “H” or “L” is with reference to the energy being high or low).
The absorption coefficient of the medium in Fig. 8 is controlled via a fast signal pulse with PSIG-IN entering the right side of the top waveguide. The medium can be provided by a semiconductor medium with bandgap energy EG [11, 12]. For 1550nm wavelength range, a commonly available medium is Indium Phosphide (InP) based ternary and quaternary (e.g. InGaAs/InGaAsP) III–V semiconductor quantum wells.
At the initial state, a CW beam PPS-IN at λH, with photon energy EH >EG, enters PS-IN (EH=hc/λH). This CW beam functions as a “power supply” beam and is labeled as PS. For the desired operation, we make PPS-IN to be substantially higher than the medium saturation power PSAT so that it will initially saturate M (i.e. pump M to transparency at λH) and be fully coupled to PS-OUT as shown in Fig. 9(a), resulting in PPS-OUT=PPS-IN.
Transparency at λH means that M is having population inversion (gain) for a beam with lower photon energy at λL due to the way electrons are filled in the band structure as illustrated by the band diagram on the right side of Fig. 9(a). Transparency means about half the electrons are excited to the conduction band and hence the lower energy region in the conduction band shall be filled by more than half the electrons transferred from the valence band to the conduction band at the same k-state in the momentum space. When a short signal pulse PSIG-IN at λL with a lower photon energy EL<EH (still above EG; EL=hc/λL) enters SIG-IN/ PS-OUT, it will see gain and de-excite M via stimulated emission. This causes M to become lossy at λH and the PPS-IN beam will see loss in the top waveguide. Due to AMOI, the PPS-IN beam will be partially channeled to exit the bottom waveguide at SIG-OUT with a short pulse PSIG-OUT at λH (Fig. 9(b)). Thus, a signal pulse at λL entering SIG-IN/PS-OUT will produce an output pulse from SIG-OUT with λH<λL, resulting in energy-up conversion. The switched out pulse at SIG-OUT can actually have higher power than the input pulse to SIG-IN, resulting in signal amplification.
As the switching-on operation is based on stimulated decay by the input signal beam, the switching “ON” can be fast. Likewise, as the switching-off operation is based on saturation by the power supply beam, the switching “OFF” can be fast. Thus, the use of absorption to affect optical interference in this EUPT case enables us to evade the typical slow operation due to carrier spontaneous decay.
From analytical results shown in Fig. 5, we see that the longer the coupling length LC, the more we can switch out the power-supply beam power. However, a longer LC will result in a larger device. A good trade-off length is when the power-supply beam is switched out about 20–30% or at αLC ~5–7 (α is the absorption coefficient when M is totally de-excited). It is a good trade-off as although the loss is high at this region, the αLC value is low so the device size can be short. At the same time the operation power can be low since the total amount of active medium to be excited or de-excited is relatively small. If αLC is further reduced the portion of energy converted from power supply to output signal will be very low, if αLC is increased the optical power needed for the same operation speed will increase and the device size will also increase. Typical direct-gap semiconductor can have α~0.5µm-1, resulting in compact device size of LC ~10µm.
5.2 The energy-down photonic transistor (EDPT)
While EUPT outputs a pulse at λH with an input pulse at λL, energy-down photonic transistor (EDPT) will be able to convert the pulse back to a wavelength λLa near or at λL. Next, we describe the all-optical operation of the EDPT. The structure of the EDPT is shown in Fig. 10. The device has various input/output ports labeled as PS-IN, SIG-IN, PS-OUT, and SIG-OUT.
To function as an energy-down photonic transistor, a CW optical power-supply beam λLa at close to the bandgap energy is sent into the left side of the top waveguide. This beam will then be coupled to the bottom waveguide and exit the right side of the bottom waveguide. This CW beam functions as the “power-supply” beam for the energy-down photonic transistor. In this example, the CW power-supply beam is assumed to be at λLa wavelength. As the power-supply beam misses the medium in the upper right, the medium is in lossy state at λLa. This is illustrated by the band diagram in Fig. 11(a).
When an input signal pulse at λH is sent into the right side of the top waveguide, the signal will excite the active medium, resulting in population inversion and can provide optical gain for a longer wavelength that is still above the bandgap energy. This is illustrated by the band diagrams in Fig. 11(b). The result is that λLa now sees gain at the last half of the top waveguide, which causes part of its energy to remain at the top waveguide and exit the top waveguide on the right. The net effect is a wavelength translation of an optical pulse from λH to λLa. This “gain” induced switching is due to gain manipulation of optical interference (GMOI) and is the specific switching mechanism on which EDPT is based. Note that the signal pulse can also be launched into the device from the left side of the bottom waveguide. The beam will be partially coupled to the active medium region and excite the medium, resulting in the output of λLa pulse at the right side of the top waveguide.
It turns out that in this EDPT case, the power-supply beam switched out depletes nearly all the carriers that were excited by the photons in the signal beam. Hence, the number of photons switched out can only at most equal the number of photons from the input signal pulse. As a result, the most one can achieve is near-unity quantum efficiency (one photon in gives one photon out with one excited electron in M’ as the intermediate state). However, there is power loss as the switched out wavelength is longer than the input signal wavelength (i.e. the switched out power-supply beam is at a lower photon energy than the input signal beam).
As the switching-on operation is based on medium excitation by the input signal beam, the switching “ON” can be fast. Likewise, as the switch-off operation is based on stimulated decay by the power-supply beam, the switching “OFF” process can be fast. Thus, the use of gain to affection optical interference in this EDPT case enables us to evade the typical slow operation due to carrier spontaneous decay.
From the analytical results shown in Fig. 7, we see that the longer the coupling length LC, the more we can switch out the power-supply beam power. However, a longer LC will result in a larger device. A good trade-off length is when the power-supply beam at port SIG-OUT is about the same as port PS-OUT or at αLC ~7 (α is the absorption coefficient when M’ is totally de-excited). Typical direct-gap semiconductor can have α~0.5µm-1, resulting in a compact device size of LC ~14µm.
6. Full dynamical simulation of high speed operations based on numerical method
In order to model the high-speed transient operations of the EUPT and EDPT, we use a sophisticated multi-level multi-electron (MLME) FDTD medium model capable of modeling the carrier dynamics in semiconductor medium [12, 13]. We will give a brief summary of this MLME model in section 6.1. The MLME model is used to simulate the high-speed response of the EUPT and EDPT under fast pulse operations with realistic semiconductor medium parameters in section 6.2 and 6.3, respectively. Sub-10ps rise and fall time is observed for both the EUPT and EDPT. In section 6.4, we discuss the layout of the full photonic transistor with combination of the EUPT and EDPT. At last, in section 6.5 we compare the spectrum performance of the proposed photonic transistors with typical switching device based on χ (3) medium.
6.1 Multi-level multi-electron FDTD for high-speed simulation of EUPT and EDPT
The EUPT and EDPT devices can be realized using semiconductor materials. To model the transient operations of the proposed EUPT and EDPT devices with realistic semiconductor material properties having complex electron dynamics, we employ the multi-level multi-electron FDTD (MLME-FDTD) model [12, 13, 14] developed recently by us.
The MLME-FDTD model is capable of modeling the sophisticated semiconductor electron and hole dynamics in the conduction and valence bands, including carrier band filling, carrier dynamics, and carrier thermalization. The theory is based on a multi-level multi-electron model shown in Fig. 12(a). The details of the model are discussed in . Several pairs of discrete energy levels are used to model the semiconductor band structures and are denoted by i_c for conduction band and i_v for valence band. The density of state at each level is denoted by N0 Ci or N0 Vi. Interband optical transition and intraband non-radiative transitions are allowed in the model. The model can be used to simulate the interaction of the active media with multiple beams at multiple wavelengths (e.g. at λH and λL). The absorption spectrum at different carrier densities are plotted out in Fig. 12(b) for multiple pairs of levels spaced at 25nm in wavelength. The simulator reproduces what is expected from band filling.
6.2 High-speed operation of the EUPT
The full high-speed device simulation of the EUPT with device transient dynamics requires the pulse-medium interactions to be simulated with the pulse’s spatial propagation. This spatial-temporal simulation can be performed using the MLME-FDTD model discussed above. The simulation assumes the following typical semiconductor parameters : spontaneous decay time τSP=1nsec, intraband relaxation time τ’=100 fsec, dipole transverse relaxation rate δω=3.9×1013 Hz, and a ground-state electron population density that gives an on-resonance absorption coefficient of α=0.6 µm-1 and ISAT=1kW/cm2, which are within typical experimental values .
As an example of the all-optical operation, we assume LC=15µm. The structure is a single-mode semiconductor waveguide with a high refractive index core material with n=3.4 (typical for III-V semiconductor) surrounded by low refractive index cladding material with n=1.45 (e.g. SiO2). For the simulation, we assumed TM modes, a waveguide width of 0.25 µm, and a waveguide height of 0.35 µm, similar to the nanoscale waveguide structure used the photonic-wire laser shown in , which was realized experimentally. This small nanoscale waveguide cross-section gives a calculated mode area AWG of 0.043 µm2 (for λH=1450 nm) or PSAT=0.43 µW. We take λL=1550 nm, λH=1450 nm, PPS-IN=3,000PSAT=1.29 mW. As the power requirement of the device is proportional the intensity of the pulse times the mode area, using a small mode area leads to smaller power requirement. Using the small mode waveguide structure allows us to demonstrate the possibility of very low power operation. The fabrication of the waveguide with such dimensions has become a routine in present photonics research .
At SIG-IN, we sent in a 50 psec signal pulse (20Gb/s) with a pulse peak power PSIG-IN and obtained the output pulse PSIG-OUT (see Fig. 13(a)). We then tabulated the output signal pulse peak power PSIG-OUT against the input signal pulse peak power PSIG-IN in Fig. 13(b) by joining the discrete data points obtained from the MLME-FDTD simulations. Thus, Fig. 13(b) shows the signal output peak power as a function of the signal input peak power, from which we see a few very interesting results as follows:
(a) Signal switching gain: at a signal input peak power of 20µW, the signal output peak power is 300 µW (see the inset), indicating a total signal power switching gain of over 15.
(b) Quasi-linear regime: at signal input peak power of 10–50µW, the output power increase somewhat linearly with the input power. This quasi linear regime (10–50µW) is followed by a transition regime (50–150µW) and then a saturation regime (>150µW).
(c) Saturation regime: at high signal input peak power of >150µW, the signal gain goes down to below 3 (PSIG-IN=0.15-1.5 mW) in which the output changes by only 15% with the input changes by 10x.
(d) The involvement of “absorption” for switching makes the device analogous to the “transfer resistance” used in electronic transistors. This is because “absorption” is like “resistance” for photons and electronic transistors do not make use of higher-order nonlinearity for electron wave to achieve switching. In comparison, χ (3) based devices use higher-order nonlinearity for optical wave to achieve switching that is nothing like the transfer resistance used in electronic transistors.
It would be interesting to examine the input/output pulse temporal shapes for the SIG-IN and SIG-OUT pulses at the quasi-linear regime. The result is shown in Fig. 13(a) in which the input pulse is an ideal square pulse with a peak power of 50µW. We see that the output pulse is a near-square pulse with a 20%–80% rise time of 2.1psec and 80%–20% fall time of 5.7psec. The device could potentially operation at speed ~100Gbit/sec.
6.3 High-speed operation of the EDPT
High-speed operation is again simulated spatial-temporally using the MLME-FDTD method. Our dynamical simulation with a 50psec input pulse at λH=1450nm and peak power PSIGIN=0.43mW is shown in Fig. 14(a). The waveguide and medium parameters are the same as those for the EUPT above. Figure 14(b) plots the output pulse peak power versus input pulse peak power with a power-supply power of PPS-IN=14µW (at λLa=1550nm). From Fig. 14, we see a few very interesting results as follows:
(a) No signal gain but near-unity quantum efficiency: we see that while EDPT has no signal amplification, high-efficiency conversion (>75%) in terms of switching power can be achieved, which gives near-unity quantum efficiency (>85%) after accounting for the decrease in photon energy from the input to the output. Note again that the power-supply beam would not be self switched irrespective of how high its power is.
(b) Signal output power mainly from signal input power: The signal output peak power in Fig. 14(b) can go as high as 0.3mW while power supply input power is only 14µW. Thus the power supply input undergoes substantial optical gain of over 10x when it is switched out. It basically only serves as a “seed photon source” that depletes the excited carriers in M’. The excited carriers in M’ are from the carriers excited by the input signal photons.
(c) Quasi-linear regime: at signal input peak power of 50–500µW, the output power increase somewhat linearly with the input power. This quasi linear regime is followed by a transition regime (500–750µW) and then a saturation regime (>750µW).
(d) Saturation regime: at high signal input power of >1mW, the signal output power actually saturates and decreases.
(e) Temporal response: the input pulse in Fig. 14(a) is an ideal square pulse with a peak power of 430µW. We see that the output pulse is a near-square pulse with a 20%–80% rise time of 4.2psec and 80%–20% fall time of 5.9psec. The device could potentially operation at speed ~100Gbit/sec.
6.4 Full photonic transistor with EUPT and EDPT
The EUPT and EDPT can be joined in tandem as shown in Fig. 15(a) to achieve a full photonic transistor (FPT) capable of wide wavelength conversion range, signal amplification, and pulse regeneration with the cascaded input/output relation shown in Fig. 15(b). The device can operate within the wavelength range defined by the wavelengths of the two power-supply beams from λLa to λH. The input signal is at λL that has to be at lower energy than λH. The output wavelength at λLa can be at any wavelength around λL (at higher, lower or the same energy as λL). The EUPT as well as the FPT device behaves similar to an electronic transistor in that it is capable of signal power gain. It has both a linear and a saturation amplification regime in the response curve. The “power supplies” of EUPT, EDPT, and FPT are CW optical beams, switched to the output via input signals by means of optical absorption or gain. In input-output block diagram form, the Photonic Transistors are like the Electronic Transistors but with “power-supply currents” replaced by “CW optical beams”. The use of two CW optical beams at different wavelengths provides wavelength conversion and is unique to the optical case. There is no electrical power needed for the Photonic Transistors to function. The “power supplies” to a photonic transistor circuit are just CW optical beams. Like transistors, logic gates can be formed via cascading EDPTs and EUPTs to realize various all-optical signal-processing functions. In such applications, some of the CW beams will be replaced by other input pulse streams.
6.5 Spectrum performance of the photonic transistors and comparison with χ(3) medium
It is well known that χ (3) medium based all-optical devices have spectral broadening problem at close to and above π phase shift if the pulses involved are non-square pulses. In fact, pulses in optical networks are typically Gaussian in shape. It would be of interest to investigate the spectral performance of EUPT and EDPT and compare them to that of χ (3) medium based all-optical devices, especially for the case in which the pulses involved are Gaussian pulses.
To model the operation of the proposed EUPT and EDPT devices with real semiconductor material, we employ the recently developed multi-level FDTD model. For the simulation below, a total of five dipole pairs with wavelengths of 1550nm, 1500nm, 1450nm, 1400nm, and 1350nm are used to describe the band structure. We use a simple parabolic band structure as described in [13, 14].
In the discussions for EUPT and EDPT, we assumed bulk active medium with a ground-state absorption coefficient of α=0.5µm-1 and the guided optical field is almost completely overlapping with the active medium. Here, as a variation, we take the case of an active medium composed of quantum wells in the waveguide. For this quantum-well medium case, the waveguide structure is assumed to have an overlapping coefficient of 10% with the thin quantum wells (typical value for ~5 quantum wells with width of 5nm each). As a result, the effective absorption coefficient is more like α=0.05µm–1. The total coupling length is designed to be 150µm, giving αLC of ~7.5.
We simulated the pulse operation of the EUPT device with Gaussian pulses. The power-supply beam is at wavelength of 1450um with power of 4.3mW. The input signal pulse has 1/e2 Gaussian pulse width of 100ps and peak pulse power of 0.043mW at wavelength of 1550nm as shown in Fig. 16(a). The output pulse is also plotted out in Fig. 16(a). The input/output pulse spectrum is compared in Fig. 16(b). The output pulse suffers slight broadening from the medium response time. However, the Gaussian-like pulse shapes in both temporal and spectral domain are retained quite well. And the switching has a gain of ~14.
Next we also simulated the pulse operation of the EDPT device with Gaussian pulses. The power-supply beam is at wavelength of 1550nm with power of 0.43mW. The input signal pulse has 1/e2 Gaussian pulse width of 100ps and peak pulse power of 4.3mW at the wavelength of 1450nm as shown in Fig. 17(a). The output pulse is also plotted out in Fig. 17(a). The input/output pulse spectrum is compared in Fig. 17(b). Again, the EDPT device is able to retain the near Gaussian pulse shapes in both temporal and spectral domains quite well. And the switching has power efficiency of ~58%.
For the purpose of comparison, we also simulated the case of a χ (3) medium switch with Gaussian pulse. Significant power switching requires π phase shift to be achieved at the peak of the Gaussian pulse. The χ (3) medium has a χ (3) coefficient of 2.8×10-16m2/V2 and the structure involved is a weakly guiding optical waveguide with core refractive index of 3.55 and cladding refractive index of 3.5. The total length of the χ (3) medium is 100µm, so a Gaussian pulse with peak intensity of 1.2×108 W/cm2 will experience π phase shift. The optical spectra for the pulses before and after the switch are shown in Fig. 18. We see that the pulse spectrum after passing through the medium is significantly broadened and also exhibits three small peaks, which is the well-known characteristic spectrum for Gaussian pulse that has experienced cross-phase modulation of π at its peak.
From these simulations we see that the GAMOI based photonic transistor devices show obvious advantages in retaining the original spectrum profile of the input pulse. The minimal changes in the signal pulse spectra for the GAMOI based photonic transistor devices also show that the main switching mechanics of these devices is the gain or absorption modulation, instead of the refractive index changes.
7.1 Figure of Merits for All-Optical Devices, and Comparisons with Electronics
To measure how well the photonic transistors perform, we suggest the use of a multi-dimensional Figure-of-Merits (FOM) given by
which takes into account the Photonic Transistor’s power-supply power PPS, control-signal power PCTR-SIG, device area A, operating bit rate R=1/T, and signal amplification GS (GS<1 is loss). The factor (PCTR-SIG + PPS)/R≡PTOTT is the total energy consumed per bit during switching. It also takes into account the optical bandwidth (dv) of the PT under wavelength division multiplexing through Nch, defined by Nch=dv/R, which is the number of optical channels that can be packed within dv for bit rate R. This enables us to incorporate the broader band advantage of optical devices in some way even though at any one time, only one channel can be processed by a PT. This is a somewhat reasonable definition as it will give a larger FOM for device with smaller device area, and power dissipation per bit. It will also give a larger FOM for higher device gain, higher operating bit rate, and higher number of optical wavelength channels.
Applying the FOM so defined to a typical electronic transistor in a microprocessor , we have R ~3.8GHz, Nch=1, P ~0.24mW (V ~1.1 Volt, Ion ~1.38mA/µm), GS ~2, A ~0.0256µm2 (160nm transistor pitch), giving for the electronic transistor an equivalent MFET=(3.8×109×2)/(0.24×10-3×0.0256×10-12) (J-1m-2)=1.2×1027(J-1m-2).
A Relative Figure-of-Merits normalized to the typical Electronic Transistor (ET) can then be given by dividing MFPT by MFET. It will be referred to as the Photonic Transistor Relative Figure-of-Merits: FPT=MFPT/MFET. The desired PT device shall have FPT value approaching or exceeding 1 to be competitive with electronic transistors.
In Table 1, we show the estimated FPT for some exemplary all-optical switching devices based on χ(3) and SOA, and compare them to those based on GAMOI, The χ(3) case taken is GaAs at below half the bandgap energy. In the Table, we assume the use of nanoscale waveguides for both the χ(3) case and the GAMOI case. The SOA case assumes the typical weakly-guiding waveguides. The results in Table I show that the typical χ(3) and SOA n (2) based devices have low FPT’s with FPT ~10-8, respectively, based on parameters in [3, 4, 7–9]. Whereas the PTs described here can achieve a FPT near 0.01 or over 105× higher than the typical χ(3) or n (2) based devices based on the simulated results. While the simulated results are not experimental results, they are based on realistic semiconductor parameters such as the material’s saturation intensity, gain, and spontaneous decay time for actual semiconductor materials. Their high FPT thus indicates the potential attractiveness of the PT devices described here.
Note that for the GAMOI based photonic transistors, we use the typical semiconductor waveguide structure for the MF estimation. Low overlapping of the optical mode and the active materials are assumed (10% overlapping) so the resulted device length is long, leading to large device areas. If bulk active medium with high overlapping is assumed, the device length will be much more compact (the total length can be reduced by 10× as the effective absorption coefficient will be 10× higher), further increase the F of the PT to MF~0.12, only 10x smaller than that of present-day highly-optimized electronic transistors. Meanwhile, further engineering of the active medium can also improve the device power consumption. For example, if the spontaneous decay time of the active medium can be reduced, the device speed can improve. The optimization of the band structure could also reduce the saturation intensity, leading to lower operating power. Hence, the Figure-of-Merits for the GAMOI based Photonic Transistors could be higher when further optimized.
7.2 Summary and discussion
In summary, the main problem currently impeding the realization of practical Photonic Transistor (PT) is that the physical schemes involved typically require either high optical power or long interaction length and had problem achieving switching gain, resulting in low Transistor Figure-of-Merits (FPT). In this paper, we illustrated a new physical mechanism to realize Photonic Transistor (PT) with the use of optically-controlled gain or absorption to manipulate optical interference (GAMOI), resulting in highly-efficient all-optical operations with switching gain that can be used to form PTs with a wide variety of functionalities (switching, amplification, logical operation, λ conversion, pulse regeneration). The illustrated use of coupled waveguides is not the only choice as other multimode optical interference devices can also be used. Simulation of exemplary devices based on typical semiconductor medium show that the PTs could potentially operate at high speed of ~100Gb/s, low signal operating power (hundreds of µW), low power consumption (a few mW), compact size of ten of micrometers, good signal amplification, and broad optical bandwidth. These devices could have a Transistor Figure-of-Merits >105 times higher than current χ(3) approaches. In terms of device physics, the use of absorption and gain make the PTs closer to the “transfer resistance” used in electronic transistors. The closely located active and passive waveguide can be fabricated by using either high resolution quantum well intermixing process, or by using specially designed wafer structure such as offset quantum well structure  whereby the active and passive region can be precisely defined to sub-micron accuracy. The operating power and speed performances are also dependant on the medium properties such as saturation intensity and spontaneous decay time, which may be further engineered using quantum-confined structures. In conclusion, the new device concept described and simulated here will enable various new possibilities for realizing multi-functional Photonic Transistors that are orders of magnitudes more efficient than current approaches, and are highly attractive.
The work is supported by NSF under Award No. ECS-0501589, by NSF MRSEC program under grant DMR-0076097, and by the NASA Institute for Nanoelectronics and Computing under Award No. NCC 2-1363.
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