Patent Application
20130155491
The present invention is directed, in general, to optical signals.
Parametric signal processing in a fiber is typically based on four-wave mixing (FWM). Devices based on such techniques can typically amplify, frequency convert (FC), phase conjugate, regenerate and sample optical signals in communication systems. One particular implementation of such frequency conversion is the so-called Bragg scattering (BS) which is also a technique known in the related art.
BS, as known in the related art is a frequency conversion process based on nondegenerate FWM in which a sideband (signal) photon and a pump photon are destroyed and different sideband (idler) and pump photons are created.
BS is a versatile process capable of providing tunable and low-noise FC for classical optical signals or single photons. In the context of the present invention, a classical signal is to be understood to refer to a signal which contains many photons and is in general governed by the laws of classical physics. An example of such classical signals is signals in conventional (i.e. deployed) communication systems. Single photons, in contrast, are governed by the laws of quantum mechanics.
Not only does BS allow for transfer of power (photon flux) from the input signal to the output idler, it also transfers the quantum state. For example, if the input photon is entangled with another quantum degree of freedom, so also will be the output photon.
Embodiments of the present disclosure are related to BS signal processing with the aim of providing efficient regeneration and reshaping of an optical signal which may improve the quality of transmission and detection of the optical signal and facilitate the use of pulse-shape coding. In systems employing pulse-shape coding, each orthogonal pulse shape may represent a different symbol. BS allows for adding and dropping information from specific channels, and exchanging information between channels, in such systems.
Some embodiments of the disclosure relate to a method of processing an optical signal comprising:
According to some specific embodiments, the first pump waveshape is chosen so as to maximize interaction of said pulsed pump signal with the input optical signal thereby producing a shape for an output idler signal, corresponding to the second pump waveshape.
According to some specific embodiments, the method further comprises an FWM process thereby producing a frequency-shifted idler being a conjugated copy of the input optical signals thereby converting a frequency of the idler to a frequency of the input optical signal.
According to some specific embodiments frequency conversion is applied to the input optical signal prior to inputting the combined optical signal into a nonlinear optical material.
According to some specific embodiments, the method of frequency conversion and reshaping is applied to pulses containing arbitrary numbers of photons.
Some embodiments of the disclosure relate to an apparatus for processing an optical signal comprising:
According to some specific embodiments, the coupler comprises a first coupler for combining the first pulsed pump signal with the second pulsed pump signal thereby generating a combined pulsed pump signal and a second coupler for combining the combined pulsed pump signal with the input optical signal.
According to some specific embodiments, the coupler is a three-way coupler adapted for combining the first pulsed pump signal, the second pulsed pump signal and the input optical signal.
For a more complete understanding of the present disclosure, reference is now made to the following description taken in conjunction with the accompanying drawings, in which:
a and 1b illustrate frequency diagrams of Bragg scattering processes according to some embodiments.
a through 4e are exemplary graphical representations of amplitude profiles, under noisy conditions, of an optical signal (
Embodiments of the present disclosure relate to the use of BS in order to regenerate and reshape optical signals.
Herein, the terms “regenerate” or “regeneration” are to be understood to relate to techniques of reducing noise on an optical signal. Likewise, the terms “reshape” or “reshaping” are to be understood to relate to techniques of changing the shape or format of an optical signal.
In BS, the conservation of energy and momentum are typically manifested by the frequency-matching and wavenumber-matching conditions. BS is driven by pump-induced nonlinear coupling and suppressed by dispersion-induced wavenumber mismatch. Therefore, it may be desirable to determine the conditions under which BS is wavenumber matched.
Some solutions for obtaining wavenumber match are discussed in articles by C. J. McKinstrie, J. D. Harvey, S. Radic and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Optics Express 13, 9131 (2005) and H. J. McGuinness, M. G. Raymer, C. J. McKinstrie and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Physical Review Letters 105, 093604 (2010)> The content of both of these articles is incorporated herein by reference in its entirety.
BS may be configured to generate waves whose frequencies may be substantially symmetric about a zero-dispersion frequency. When two pumps are used for optical wave generation, one pump may co-propagate with the input optical signal, whereas the other pump co-propagates with the idler thereby enabling reshaping functions as will be described in further detail below.
OPPA 200 has a first pump-wave source 201 and a second pump-wave source 202. Herein each one of the pump-wave sources may also be referred to as pump source or simply pump. The pumps 201 and 202 may be of any known type such as for example a laser source.
OPPA 200 further comprises a first coupler 203 and a second coupler 204. The first coupler 203 is coupled to the first pump 201 and the second pump 202 on the one hand, and to the second coupler 204 on the other, as shown in
The first pump 201 and the second pump 202 are configured to generate respective short pulsed signals. The pulsed pump signal generated by the first pump 201 has a first waveshape, whereas the pulsed pump signal generated by the second pump 202 has a second waveshape. The specific waveshape of each of the pulsed pump signals is chosen so as to maximize interaction with an input optical signal S and to produce the desired shape for an output idler signal I, as will be described din further detail below.
The pulsed pump signals output form the first pump 201 and the second pump 202 are input into the first coupler 203. The coupler 203 combines the two pulsed pump signals and inputs the combined pulsed signals into the second coupler 204.
Assuming that an input optical signal S propagating through the optical fiber 205 is also input into the second coupler 204 as shown in
In an alternative embodiment, a three-way coupler may be used to combine the optical communication signal with the two pump waves.
The combination of the input optical signal S and the pulsed pump signals (herein referred to as combined optical signal) is then output from the second coupler 204 and input into a nonlinear optical material 206. The nonlinear optical material 206 is characterized by a nonlinearity coefficient and a set of dispersion coefficients. These characteristics give rise to a frequency conversion based on parametric processing of the combined optical signal propagating inside the nonlinear optical material by Bragg scattering (nondegenerate FWM).
As a consequence, a sideband signal photon and a pump photon are destroyed and a different sideband signal photon (herein referred to as idler signal) and a pump photon are created. The nonlinear optical material may be of any known material. Some examples may be centrosymmetric media having third-order nonlinearities, for example optical fibers made of silica, bismuth and chalcogenide; other examples may be silicon waveguides (with third-order nonlinearities) and lithium-niobate waveguides (with effective third-order nonlinearities from cascaded second-order nonlinearities).
Assuming that one of the pump signals is configured to co-propagate with the input optical signal S and the other one of the pump signals is configured to co-propagate with the idler signal, the idler signal may be generated such that it has an amplitude profile proportional to the amplitude of the input optical signal and a shape corresponding to the second pump waveshape.
The above configuration of the OPPA 200 allows, on the one hand, for providing an amplitude for the output idler which is proportional to that of the input signal, and on the other, determine the shape-function of the output idler as such shape may correspond to the shape-function of the co-propagating pump. In fact, determining the shape-function of the co-propagating pump provides the further advantage of ability to reshape the output idler arbitrarily, according to any desired shape. This is explained in the following description.
Supposing that the pump and sideband frequencies are chosen so that the conditions for frequency-matching and wavenumber-matching, as mentioned above, are satisfied. Then the sideband evolution is known to be governed by the so-called coupled-mode equations:
(∂z+βr∂t)Ar(t,z)=iγpq(t,z)As(t,z), (1)
(∂z+βs∂t)As(t,z)=iγpq*(t,z)Ar(t,z), (2)
where Aj is a slowly-varying wave (mode) amplitude, p and q represent first and second pumps, z denotes distance, t denotes time, s relates to signal sideband, r relates to idler sideband, ∂ denotes derivative such that ∂t=∂/∂t is a time derivate and ∂z=∂/∂z is a distance derivative and βj is an abbreviation for the group slowness β1j, wherein the number 1 denotes the first order, namely the first term in the Taylor expansion of the dispersion function.
The coupling strength is represented by γpq such that γpq=2γApA*q where γ is the Kerr nonlinearity coefficient, and Ap and Aq are pump amplitudes (wherein i=√(−1) and * is a complex conjugate). The effects of intra-pulse dispersion and pump-induced cross-phase modulation have been neglected, because these effect are typically weak for a wide range of relevant system parameters. Equations (1) and (2) apply to scalar FWM, which involves waves with the same polarization. Similar equations may apply to vector FWM, which involves waves with different polarizations.
The pumps are not affected by the sidebands, so they convect through the nonlinear optical material, for example through a highly nonlinear fiber, with substantially constant shape. In the low-conversion-efficiency regime, the input signal seeds the growth of a weak idler, whose presence does not affect the signal significantly, so the input optical signal also convects through the fiber with substantially constant shape. Hence, the pump and signal amplitudes can be written in the following form:
A
j(t,z)=ajfj(t−βfz), (3)
∫−∞∞|θj(t)|2dt=1, (4)
in which case the amplitude aj is the square root of the pulse energy. The idler equation can be written in the following form:
(∂z+βr∂t)Ar(t,z)=i2γAp(t−βsz)Aq*(t−βrz)As(t−βsz) (5)
where the terms on the right side are specified functions. Assuming that the retarded time t−βrz is represented by τ, then the idler equation is expressed as follows:
∂zAr(τ,z)=i2γAp(τ+βrsz)As(τ+βrsz)Aq*(τ) (6)
Where βrs=βr−βs>0 is the differential slowness (walk-off). By integrating Eq. (6), in which z is a parameter, one finds the following expression for the output idler:
A
r(τ,l)=i2γ∫0lAp(τ−βrsz)As(τ−βrsz)dzAq*(τ). (7)
Equations (3) and (7) imply that the amplitude of the output idler Ar is proportional to the amplitude of the input signal As, so information is transferred from the input optical signal to the idler. The shape of the output idler depends on the shapes of the input pumps signals. If the input durations are significantly shorter than the walk-off time βrsl, then the waves may collide entirely within the fiber. In fact, the requirement that the collision be complete imposes a minimal-length requirement on the fiber. In such case, the integral in Eq. (7) does not depend on τ and the shape-function of the output idler is the conjugate of the shape-function of pump q (which co-propagates with the idler). The interaction between the input optical signal and pump p co-propagating with the input optical signal (namely, the efficiency with which they drive FWM, i.e. idler generation) is strongest if their shape-functions are conjugates of each other, in which case the following expression applies:
A
r(t,l)=i(2γapaq*/βrs)as∫q*(t−βrl,0). (8)
Equation (8) shows that the conversion efficiency is proportional to the nonlinearity coefficient and the product of the pump amplitudes, and is inversely proportional to the walk-off (If βp differs slightly from βs, the conversion efficiency is reduced slightly.)
As stated above, the amplitude of the output idler is proportional to that of the input signal. Furthermore, the shape-function of the output idler is specified by the shape-function of the co-propagating pump (not the input optical signal). This pump shape-function could be the same as, or different from, the input optical signal shape-function. Hence, the output idler can be reshaped arbitrarily relative to the input signal. In particular, the amplitude fluctuations associated with a noisy signal can be removed. Similar results apply to the generation of an output signal by pumps and an input idler.
In the following, three examples of idler generation and signal reshaping are considered. Time is measured in units of the common pump duration (root-mean-squared width) σ, amplitude is dimensionless and distance is measured in units of σ/βr. For these conventions, group slowness is measured in units of βr and the interaction length βrl/σ is the ratio of the idler transit time to the pump duration. The pumps and signal have Gaussian or rectangular shape-functions. All of the following results were obtained by integrating Eq. (7) numerically, for the case in which βs/βr=−1. This relation is valid in a frame moving with the average group speed of the sidebands. Consistent with Eq. (8), the idler amplitude is measured in units of i2γapaq*/βr.
In the first example, all three input pulses (both pumps and the input optical signal) are Gaussian, and are timed to collide (overlap completely) substantially in the middle of the fiber. The idler generated by these inputs is illustrated in
In
In the previous example, the input signal was assumed to be a perfect noiseless Gaussian. However, real signals are usually degraded by noise.
The second example therefore relates to noisy conditions.
The amplitude of the output idler at time t depends on the amplitude of the input signal at time t′, where t−βr≦t′≦t−βsl. As the interaction length increases, so also does the number of input signal values on which the output idler value depends (input signal values are meant to refer to signal amplitudes at different instants of time).
Since these input values are statistically independent, the variance of their sum increases (at most) linearly with distance, so the deviation of their sum increases as the square root of distance. Hence, the idler fluctuations increase less rapidly than the mean amplitude, so the idler profile is smoothed.
It should be emphasized that pulsed frequency conversion regenerates the pulse shape, but does not regenerate the pulse peak-amplitude. This process is complementary to gain-saturated amplification, which removes peak-amplitude variations from a sequence of pulses, but distorts the pulse shapes, therefore a choice may be made as to which process is preferred for use according to the specific application on a case by case basis. Furthermore the two processes may be used in combination if required.
In the third example, the input optical signal and its co-propagating pump are Gaussian, whereas the other pump is rectangular. The idler generated by these inputs is illustrated in
The output idler has substantially the same shape as the pump q. As the shape of the second pump q may be chosen arbitrarily, an arbitrary reshaping process therefore becomes possible.
As shown in
By combining the effects demonstrated in the last two examples, one can simultaneously regenerate and reshape a noisy input signal, or a collection of noisy input signals with the same carrier frequency or different carrier frequencies. The fiber should preferably be long enough that each pump-sideband collision is complete, but short enough that the input optical signal (idler) from one collision does not intersect the idler (signal) from the next collision. In this context long may be understood to satisfy the following relations βrl/σ>>1, wherein preferred values may be in the range of βrl/σ>4.
For some applications, it is disadvantageous to have the output idler (copied and reshaped signal) at a frequency different from that of the input signal. This problem can be solved by subsequent frequency conversion. In addition to BS, which produces frequency-shifted idlers that are direct copies of signals, use may be made of a degenerate FWM process called modulation interaction (MI) and/or a nondegenerate FWM process called phase conjugation (PC), both of which produce frequency-shifted idlers that are conjugated copies of the input optical signals. One can convert the frequency of the primary idler back to the input optical signal frequency (or any other frequency) by using any of these processes, or a combination thereof. BS driven by continuous-wave (CW) pumps produces a secondary idler that is proportional to asfq*(t), whereas MI and PC driven by CW pumps produce secondary idlers that are proportional to as*∫q(t). If necessary, subsequent FWM driven by pulsed pumps can reshape the primary idler. Alternatively, one could use prior frequency conversion to produce a (direct or conjugate) copy of the input optical signal, which would be used to drive the BS process described above. In this case, the secondary idler would be proportional to as∫q*(t) [prior BS] or as*fq*(t) [prior MI or PC].
Cross-polarization rotation can occur in materials (such as randomly-spun fibers) with tensor Kerr nonlinearities. Consider the evolution of two waves which propagate in the same direction, but have different frequencies (1 and 2), and let X and Y denote their polarization components. Then the nonlinearity that enables cross-polarization rotation couples X1 to Y2 (or Y1 to X2) in the same way that Ar is coupled to As in BS. In this process, X1 is the input optical signal and Y2 is the idler (or vice versa), each of which co-propagates with a pump (X2 and Y2) respectively.
Alternatively, consider two waves that have the same frequency, but propagate in opposite directions (1 and 2). Then the cross-polarization rotation nonlinearity still couples X1 to Y2 (or Y1 to X2) in the required manner, and each sideband still co-propagates with a pump. Hence, it is also possible, in principle, to reshape pulses by using cross-polarization rotation instead of FWM.
In fact, vector FWM and cross-polarization rotation stem from substantially the same tensor nonlinearity. If the interacting waves all have the same frequency, the resulting phenomenon is typically called cross-polarization rotation, whereas if they have different frequencies it is typically called FWM. One may consider that cross-polarization rotation is enabled by substantially the same nonlinearity that enables FWM, and has properties that are substantially similar to those of FWM. To be precise, the different polarization components in cross-polarization rotation exchange energy in substantially the same way as the different frequency components in FWM.
Although the theory of frequency conversion and reshaping was described for classical waves, similar results apply to pulses (wavepackets) containing arbitrary numbers of photons (including single photons). In the standard formulation of frequency conversion, the pumps are strong, so can be modeled classically, whereas the sidebands are very weak, so must be modeled quantum-mechanically. The Heisenberg equations for the sideband wavepackets are Eqs. (1) and (2), with the sideband amplitudes Ar and As replaced by the quantum mode operators âr and âs. Hence, the input signal and output idler operators are also related by Eqs. (7) and (8), so the quantum properties of photons are transferred from the input optical signal to the idler in essentially the same way as the classical properties of pulses. In particular, the photon wavepackets can be reshaped arbitrarily.
Finally, nonlinear optical materials may be highly nonlinear optical fibers that have direct third-order nonlinearities as well as other materials such as periodically-poled lithium niobate that have effective third-order nonlinearities produced by cascaded second-order nonlinearities. It is also possible to reshape optical signals in these materials.
In this manner, optical signal pulses may be reshaped advantageously by removing excess noise and other distortions and changing their information format (waveshape) which in turn allow for optimizing transmission through the next stage of a link or for other applications.
The solution provided herein may be implemented in relation to signal pulses in conventional communication systems as well as single-photon wavepackets in quantum information experiments. Furthermore, multiple input signals with different carrier frequencies can be processed simultaneously.
The various embodiments of the present invention may be combined as long as such combination is compatible and/or complimentary.
Further it is to be noted that the list of structures corresponding to the claimed means is not exhaustive and that one skilled in the art understands that equivalent structures can be substituted for the recited structure without departing from the scope of the invention.
It is also to be noted that the order of the steps of the method of the invention as described and recited in the corresponding claims is not limited to the order as presented and described and may vary without departing from the scope of the invention.
