We present designs of all-optical reversible gates, namely, Feynman, Toffoli, Peres, and Feynman double gates, with optically controlled microresonators. To demonstrate the applicability, a bacteriorhodopsin protein-coated silica microcavity in contact between two tapered single-mode fibers has been used as an all-optical switch. Low-power control signals (<200
There is tremendous research effort to achieve all-optical information processing for ultrafast and ultrahigh bandwidth communication and computing. The natural parallelism of optics along with advances in fabricating micro- and nanostructures has opened up exciting possibilities to generate, manipulate, and detect light and to tailor the optical molecular response for low-power all-optical computing [
A switch is the basic building block of information processing systems and optical logic gates are integral components of higher optical computing circuits. Conventional classical computing is based on Boolean logic that is irreversible, that is, the inputs cannot be inferred from the output, as the number of output bits is less than the inputs. This leads to destruction of information and hence to the dissipation of a large amount of energy [
Conservative and reversible logic circumvents this problem by having equal number of inputs and outputs and opening up the possibility of ultra-low power computing [
Several reversible logic gates have been proposed that include Fredkin gate (FG), Feynman gate, Toffoli gate (TG), Peres gate, and Feynman double gate [
However, there have been fewer designs proposed to implement other reversible logic gates. Recently, a photophysical design of a molecular Feynman gate has been proposed using fluorophores as molecular switches [
The major challenge in the practical realization of optical logic has so far been in meeting essential requirements of cascadability, fan-out, logic-level restoration, input-output isolation, absence of critical level biasing, logic level independent of loss and of course low-power operation [
Application of the extremely sensitive and versatile microresonator structures for switching and computing applications has evoked tremendous interest due to their ultra-high
Silica microcavities have inherent advantages of ultra-high
Silica microsphere optical resonators coated with a conjugated polymer [
The photochromic protein bacteriorhodopsin (BR), which is found in the purple membrane of
The BR molecule initially excited by photons undergoes several structural transformations in a complex photocycle
Recently, all-optical switching in the near-infrared with the ultra-sensitive bacteriorhodopsin (BR) protein-coated silica microcavities has been reported [
The objective of this paper is to experimentally analyze this switching configuration in more detail, by measuring the variation in the resonant shift of the TE-resonant peak of the 1310 nm IR signal by alternate exposure to green (532 nm) and blue (405 nm) pump laser beams to control the BR conformational states for faster switching, and to present general all-optical designs of various other kinds of important reversible logic gates reported in the literature, namely, Feynman gate, Toffoli gate, Peres gate, and Feynman double gate, with optically controlled microresonators. To achieve this objective, we consider the BR-coated silica microresonator switch as a template. The proposed designs offer advantages of simple configuration, cascadability, large scale-integration, flexibility and low-power operation.
Figure
(a) Schematic of the experimental set-up, (b) AFM image of bacteriorhodopsin molecules.
Two parallel single-mode fibers were tapered by hydrofluoric acid erosion and held 250
Photo-excitation of BR triggers a complex photocycle that involves isomerization and rotation of the retinal chromophore, and a proton transfer across the lipid membrane [
(a) Photo-induced molecular conformational switching between the ground and the M-intermediate states of BR, (b) IR image of 1310-nm probe beam propagation with green pump beam on and blue off, and (c) IR-probe propagation with green pump off and blue on.
In the BR-coated microcavity switch, the switching of the input signal operating at wavelength 1310/1550 nm between the output ports (2 and 4) is photoinduced with a fiber-coupled green pump laser (at 532 nm) which controls the conformational state of the adsorbed BR. Photoinduced isomerization of the retinal alters the optical properties of the BR membrane such as the absorption spectrum, the molecular polarizability, and the hyperpolarizabilities. Hence, the conformational change perturbs the optical modes interacting with BR even when there is little or no spectral overlap between the mode frequency and the BR electronic transition bands. Resonant modes in the optical microcavity significantly enhance this interaction conveying this perturbation as a frequency shift of optical resonances.
The molecularly functionalized microcavity thus redirects the flow of near-infrared light beam between two optical fibers. With the pump OFF, the probing light from input Port 1 is detuned from resonance and is directly transmitted into the output Port 2. The pump evanescently excites whispering gallery modes (WGM) propagating around the microsphere’s equator, inducing photoisomerization along their path. A low green cw laser (<200
In this experiment, green (532 nm) and blue (405 nm) pump lasers, connected to Port 1 and 3, respectively, were used to control the conformation state of the retinal. Turning the green pump on and the blue off (13-cis isomer) routes the probe into output Port 4. When the green pump is off and the blue is on (
Variation in the resonant shift of the TE-resonant peak of the 1310 nm IR signal by alternate exposure to green (532 nm) and blue (405 nm) pump beams. Inset shows the corresponding temporal switching response of a microsphere to a fast 10 kHz modulation, when green and blue pump beams (
(a) Dynamics of the ground-to-M state transformation observed by tracking wavelength shifts of TE- and TM-polarized microcavity modes on alternate exposure to green pump beam, (b) the slow thermal M-to-ground state relaxation turning into a fast photoreaction on exposure to the green pump along with the blue beam.
For the low-pump intensities used in our measurements, the maximum modulation frequency was limited to ~10 kHz, where considering the switching contrast to be defined here as the ratio of the signal change and the noise level, reduced to ~2. Enhanced switching contrast at higher modulation rates can be achieved with mode-locked green and blue pumps and higher optical densities. The switching speed of BR-based devices is limited by the timescale of the ground to M-state transition (
The ultra-high sensitivity of both microresonators and BR protein configuration results in switching at very low powers. At present, all-optical switching in BR-coated microcavity has not been optimized for practical applications. The energy/bit for switching that has been demonstrated corresponds to ~nJ/bit. Both the minimum switching energy/bit and maximum switching speed need to be ascertained by exploiting the ultrafast initial intermediates. The 200
Both green and blue pump beams can also be alternatively injected through a coupler at Port 1. Hence, the silica microcavity in contact between two tapered fibers serves as a four-port tunable resonant coupler as shown in Figure
The all-optical BR-coated microcavity switch with a single control signal at 532 nm or in conjunction with a 405 nm can be used as a building block for designing all-optical reversible logic gates, namely, Feynman, Toffoli, Peres, and the Feynman double gates. We consider a combination of three inputs, namely, the IR signal at Port 1 and 3 and the control signal at Port 1, and three outputs, that is, IR signal at Ports 2 and 4 and the control signal at Port 2.
The Feynman gate is a 2 × 2 reversible gate shown schematically in Figure
Truth table of all-optical Feynman gate.
Input | Output | ||||||||
I1 ( | I2 (mW) | NOT (I2) (mW) | O1 ( | O2 (mW) | |||||
0 | 0 | 1 | (1.5) | 0 | 0 | ||||
0 | 1 | (1.5) | 0 | 0 | 1 | (1.5) | |||
1 | (60) | 0 | 1 | (1.5) | 1 | (30) | 1 | (1.47) | |
1 | (60) | 1 | (1.5) | 0 | 1 | (30) | 0 | (0.03) |
All-optical Feynman gate, (a) block diagram, (b) schematic of the logic circuit, and (c) schematic of the design using optically controlled microcavities. The dashed line shows the option of using an inverter circuit.
The design of an all-optical Feynman gate using a BR-coated microcavity switch is as shown in Figure
Of the four input combinations, when no input is applied, the outputs are zero, due to the absence of any signal. When the control signal I1 is OFF, and the input I2 at Port 1 is ON, it passes out to Port 2 due to the inactivation of the microcavity (O2 = High and O1 = I1 = 0). Since, input at Port 1 is ON, Port 3 is OFF and so there is also no output at Port 4. When, I1 is ON and I2 at Port 1 is OFF, the input NOT(I2) at Port 3 is ON, which is switched by the microcavity to emerge at Port 2 (O2 = High and O1 = I1 = 1). Finally, when both I1 is ON and I2 at Port 1 is also ON, the signal I2 is switched by the control signal to emerge at Port 4, leading to O2 = Low and O1 = I1 = 1). Since, there is no input at Port 3 (it is OFF as Port 1 is ON), hence, it does not affect the outcome at Port 2.
We consider the experimental conditions, that is, a 200
The Toffoli gate is a universal reversible logic gate, which is also known as the “controlled-controlled-not” gate. It has a 3-bit input and output, and if the first two bits are set, it flips the third bit, as shown in Truth Table
Truth table of all-optical Toffoli gate.
Input | Output | ||||||||||||
I1 ( | I2 ( | I3 (mW) | NOT(I3) (mW) | O1 ( | O2 ( | O3 (mW) | |||||||
0 | 0 | 0 | 1 | (1.5) | 0 | 0 | 0 | ||||||
0 | 0 | 1 | (1.5) | 0 | 0 | 0 | 1 | (1.5) | |||||
0 | 1 | (60) | 0 | 1 | (1.5) | 0 | 1 | (30) | 0 | ||||
0 | 1 | (60) | 1 | (1.5) | 0 | 0 | 1 | (30) | 1 | (1.5) | |||
1 | (60) | 0 | 0 | 1 | (1.5) | 1 | (30) | 0 | 0 | ||||
1 | (60) | 0 | 1 | (1.5) | 0 | 1 | (30) | 0 | 1 | (1.5) | |||
1 | (60) | 1 | (60) | 0 | 1 | (1.5) | 1 | (30) | 1 | (30) | 1 | (1.44) | |
1 | (60) | 1 | (60) | 1 | (1.5) | 0 | 1 | (30) | 1 | (30) | 0 | (0.03) |
All-optical Toffoli gate, (a) block diagram, and (b) schematic of the design using optically controlled microcavities.
Considering the BR-coated microcavity switch described earlier, the design of an all-optical Toffoli gate is as shown in Figure
Considering the various possible combinations of the three inputs, as mentioned in Truth Table
The Peres gate is also a reversible 3 × 3 logic gate, with a schematic diagram shown in Figure
All-optical Peres gate (a) block diagram, (b) schematic of the design using optically controlled microcavities.
The design of an all-optical Peres gate with optically controlled microcavities is as shown in Figure
Case (i): Initially, when none of the inputs are applied, only P3 of M2 is high, which passes over to P4 as M2 is not activated, resulting in all output ports being low. Case (ii): When I1 = I2 = 0 and I3 = 1, both M1 and M2 are OFF and hence, O2 is low and I3 passes through to O3 and yields a high output. Case (iii): When I1 = 0, I2 = 1, and I3 = 0, again both microcavities are OFF, I2 passes over to O2 and makes it high and O3 is low. Case (iv): When I1 = 0, I2 = 1, and I3 = 1, O2, and O3 are both high as I2 and I3 get directly transmitted to these ports, without getting switched at M1 or M2. Case (v): When I1 = 1 and I2 = I3 = 0, both M1 and M2 are activated. Since I3 = 0, O3 is also low. NOT(I2) at P3 of M2 is high which gets switched by M2 to make O2 high. Case (vi): When I1 = 1, I2 = 0 and I3 = 1, again O2 is high due to switching of NOT(I2) by M2 to O2, whereas now, I3 gets switched by M1 to emerge at P4, making O3 again low. Case (vii): When I1 = I2 = 1 and I3 = 0, I2 gets switched by M2 to its P4, leading to O2 getting low, while with no I3, O3 also gets low. Case (viii): When I1 = I2 = I3 = 1, I2 and I3 get switched by M2 and M1 respectively to result in O2 and O3 getting low. The various combinations of the inputs results in the desired outputs that satisfy Peres gate logic (Truth Table
Truth table of all-optical Peres gate.
Input | Output | ||||||||||||
I1 ( | I2 (mW) | NOT(I2) (mW) | I3 (mW) | O1 ( | O2 (mW) | O3 (mW) | |||||||
0 | 0 | 1 | (1.5) | 0 | 0 | 0 | 0 | ||||||
0 | 0 | 1 | (1.5) | 1 | (1.5) | 0 | 0 | 1 | (1.5) | ||||
0 | 1 | (1.5) | 0 | 0 | 0 | 1 | (1.5) | 0 | |||||
0 | 1 | (1.5) | 0 | 1 | (1.5) | 0 | 1 | (1.5) | 1 | (1.5) | |||
1 | (60) | 0 | 1 | (1.5) | 0 | 1 | (15) | 1 | (1.47) | 0 | |||
1 | (60) | 0 | 1 | (1.5) | 1 | (1.5) | 1 | (15) | 1 | (1.47) | 0 | (0.03) | |
1 | (60) | 1 | (1.5) | 0 | 0 | 1 | (15) | 0 | (0.03) | 0 | |||
1 | (60) | 1 | (1.5) | 0 | 1 | (1.5) | 1 | (15) | 0 | (0.03) | 0 | (0.03) |
The various input-output combinations result in the realization of the Peres gate logic, as is evident from the Truth Table
The Feynman Double gate is another 3 × 3 reversible gate which maps one input to one output, while the second output is the XOR of the first two inputs and the third output is the XOR of the second and third inputs, as shown in the block diagram in Figure
All-optical Feynman Double gate (a) block diagram, (b) schematic of the design using optically controlled microcavities.
Following the criterion applied earlier, the design based on two optically controlled microcavities is shown in Figure
Truth table of all-optical Feynman Double gate.
Input | Output | ||||||||||||||
I1 ( | I2 (mW) | NOT(I2) (mW) | I3 (mW) | NOT(I3) (mW) | O1 ( | O2 (mW) | O3 (mW) | ||||||||
0 | 0 | 1 | (1.5) | 0 | 1 | (1.5) | 0 | 0 | 0 | ||||||
0 | 0 | 1 | (1.5) | 1 | (1.5) | 0 | 0 | 0 | 1 | (1.5) | |||||
0 | 1 | (1.5) | 0 | 0 | 1 | (1.5) | 0 | 1 | (1.5) | 0 | |||||
0 | 1 | (1.5) | 0 | 1 | (1.5) | 0 | 0 | 1 | (1.5) | 1 | (1.5) | ||||
1 | (60) | 0 | 1 | (1.5) | 0 | 1 | (1.5) | 1 | (15) | 1 | (1.47) | 1 | (1.47) | ||
1 | (60) | 0 | 1 | (1.5) | 1 | (1.5) | 0 | 1 | (15) | 1 | (1.47) | 0 | (0.03) | ||
1 | (60) | 1 | (1.5) | 0 | 0 | 1 | (1.5) | 1 | (15) | 0 | (0.03) | 1 | (1.47) | ||
1 | (60) | 1 | (1.5) | 0 | 1 | (1.5) | 0 | 1 | (15) | 0 | (0.03) | 0 | (0.03) |
Case (i): When none of the inputs are applied, we get no outputs. Case (ii): When I1 = I2 = 0 and I3 = 1, both M1 and M2 are not activated and hence, I3 passes over to O3 to result in a high output. The NOT(I2) which is high, also does not get switched and passes over to P4 of M1. Case (iii): When I1 = 0, I2 = 1 and I3 = 0, in the absence of any switching by M1 and M2, I2 passes over to O2 to make it high and I3 ensures that O3 is low. Case (iv): When I1 = 0, I2 = I3 = 1, since both M1 and M2 are OFF, again O2 and O3 pass over to make O2 = O3 = 1. Case (v): When I1 = 1, I2 = I3 = 0, M1 and M2 are activated and NOT(12) and NOT(I3) are now high, which get switched at M1 and M2 respectively to make O2 and O3 high. Case (vi): When I1 = 1, I2 = 0 and I3 = 1, NOT(I2) is high which is routed by M1 to O2, while I3 gets switched by M2 to emerge at P4 of M2 to result in a low output at O3. Case (vii): When I1 = I2 = 1 and I3 = 0, I2 gets switched by M1 to make O2 low and NOT(I3) gets switched by M2 to make O3 high. Case (viii): When I1 = I2 = I3 = 1, I2 and I3 get switched by M1 and M2 to result in low outputs at O2 and O3, respectively.
The above combinations result in the circuit in Figure
BR is virtually transparent at near-infrared telecom band (1310/1550 nm) [
The switching contrast can be maximized by suitably choosing the number of BR-monolayers, the photo-isomerization of which shifts the resonance to the midpoint between the original position and that of the nearest neighbor. It also increases with the increase in the polarizability. Switching can be achieved at very low powers (≤
An ideal all-optical switch requires low switching power, high speed, and high contrast. In general, high
As mentioned earlier, the transmission spectra exhibited an extinction of −9.4 dB in Port 2 and a 9.8 dB increase in transmission in Port 3. In our experimental conditions a 5 mW DFB laser operating at 1310/1550 nm was used to butt couple light into the SMF fiber. Considering ~30% light to couple through (1.5 mW) as the input signal, ~98% of the light (1.47 mW) gets switched from Port 1 to Port 4, or from Port 3 to Port 2, when the microcavity is activated and only ~2% gets coupled into Port 2 or Port 4 respectively. Considering negligible signal loss due to scattering and propagation through the short length of the connecting optical fibers, can result in cascading of a large number of switches. For instance, considering 1.5 mW of coupled light in Port 1 and a terminal signal strength of ~0.2 mW can result in principle, in cascading as many as 65 switches.
In general, the BR-coated microcavity switch is operated with outputs coded on two different wavelengths. Cascading these switches in general would require the output at one wavelength from one switch to form the input at the other wavelength for the next switch. This would then require a wavelength converter. However, as shown in the proposed designs for various Boolean arithmetic and logic circuits earlier [
An ideal photosensitive material should exhibit high sensitivity, high absorption, fast dynamics, high photo and thermal stability, and potential to tailor its properties, as coating the microcavities with a photosensitive material is of critical value. BR protein is a natural photochromic material that exhibits this unique combination of properties for practical realization. Besides its unique properties, BR is a good choice of coating a microsphere as (i) its structure is well known, (ii) it self-assembles easily onto a silica surface, (iii) its molecular configuration can be switched optically between two stable states, and (iv) a pump-probe excitation can be easily implemented. The control of all these features provides tremendous scope for tuning and optimizing the characteristics of the BR-coated microcavity switch to meet device requirements. Microcavities coated with photochromic materials such as BR have advantages in terms of simple geometry, ease of fabrication, high thermal and photostability, high fan-out, cost-effectiveness, and low-power operation.
It is extremely important that the photochromic material exhibits high fatigue resistance for practical applications. It is remarkable that BR retains its properties in film form even after being heated to 140°C whereas in liquid solutions it has been shown to be stable upto 80°C [
Recently, reversible tuning of a photonic crystal cavity resonance has been demonstrated using a thin photochromic film composed of spiropyran and polymethylmethacrylate that serves as a photosensitive cladding layer [
Recently, Directed Logic (DL) has been demonstrated as an innovative paradigm that minimizes the latency in calculating a complicated logic function by taking advantage of fast and low-loss propagation of light in integrated and waveguided on-chip photonic system [
There is tremendous research underway to fabricate high-
The proposed designs require optical excitation of BR protein, which in principle requires some energy, which due to its high quantum efficiency, high absorption coefficient, and high sensitivity, is very low. Moreover, as ultra-high-
We have presented the designs of various reversible all-optical logic gates with optically controlled microresonators, namely, the Feynman gate, Toffoli gate, Peres gate, and the Feynman double gate. To demonstrate the applicability of the designs, a basic all-optical switch has been demonstrated at telecom wavelengths, controlled with visible light, using the unique BR protein monolayers coated on a silica microresonator, coupled between two tapered single-mode optical fibers. Low-power switching has been shown, which is a consequence of the high-
The proposed designs of all-optical reversible logic gates with BR-coated microcavity can be implemented with any other photosensitive material-coated on a microresonator and in any condition in which the resonance and the coupling can be controlled externally. They can also possibly be implemented in planar geometry using integrated-optic photonic crystal micro/nanocavities. The proposed designs are general and demonstrate the applicability of using optically controlled microresonators for reversible computing applications.
S. Roy and P. Sethi are thankful to the Department of Science and Technology, Government of India, for partial support of this paper under Grant no. DST/TSG/PT/2008/04. F. Vollmer is grateful to the Max Planck Institute for the Science of Light, Erlangen, Germany, for financial support.