Single fiber bragg grating as delay line interferometer

Abstract

A delay line interferometer comprising an optical waveguide having a distributed Bragg reflector, e.g. Bragg grating, fabricated therein. The distributed Bragg reflector has a refractive index modulation with a period variation (z) along its length z that is arranged to output in transmission an output optical signal f.sub.out(t) in response to a input optical signal f.sub.in(t), wherein the output optical signal f.sub.out(t) is the result of temporal interference between one or more time-delayed replicas of the input optical signal f.sub.in(t). In other words, the distributed Bragg reflector is operable to generate and permit temporal interference between two or more time-delayed replicas of the input optical signal f.sub.in(t). The invention may thus mimic the behaviour of one or more MZIs.

Claims

1. A delay line interferometer, comprising: an optical waveguide having a Bragg grating fabricated therein, the Bragg grating having a refractive index modulation with a period variation (z) along its length z that is arranged to output in transmission an output optical signal f.sub.out(t) in response to a input optical signal f.sub.in(t), wherein the output optical signal f.sub.out(t) is the result of temporal interference between one or more time-delayed replicas of the input optical signal f.sub.in(t), wherein the optical waveguide is an optical fibre and the Bragg grating is a fibre Bragg grating (FBG), the FBG being a phase-modulated FBG and having a substantially uniform coupling strength amplitude |(z)| along its length.

2. The delay line interferometer according to claim 1, wherein the optical waveguide is arranged to support the propagation of optical radiation between an input portion for receiving the input optical signal f.sub.in(t) and an output portion for transmitting the output optical signal f.sub.out(t), wherein the Bragg grating is fabricated in the optical waveguide between the input portion and the output portion.

3. The delay line interferometer according to claim 1, wherein the optical fibre comprises: a core having a first refractive index, and a cladding layer surrounding the core, the cladding layer having a second refractive index, the second refractive index being lower than the first refractive index, and wherein the FBG comprises a refractive index modulation inscribed within the core.

4. The delay line interferometer according to claim 3, wherein the refractive index modulation is confined within the core.

5. A delay line interferometer according to claim 1, wherein the spectral response |H.sub.T()| of the phase-modulated FBG substantially corresponds to a Fourier transform of an objective impulse response h.sub.T,obj(t) of the phase-modulated FBG, where the objective impulse response corresponds to a minimum phase system.

6. The delay line interferometer according to claim 1, wherein the period variation (z) of the phase-modulated FBG is arranged to output in transmission a time-spaced series of two or more optical pulses in response to a single input pulse.

7. A method of fabricating a phase-modulated fibre Bragg grating (FBG) for a delay line interferometer, the method comprising: obtaining an objective spectral response |H.sub.T,obj()| that is a Fourier transform of an objective impulse response h.sub.T,obj(t) of the phase-modulated FBG, where the objective impulse response corresponds to a minimum phase system; selecting a coupling strength |(z)| to be exhibited by the phase-modulated FBG along its length z; calculating a grating period variation (z) for the phase-modulated FBG using the objective spectral response |H.sub.T,obj()| and the coupling strength |(z)|; and inscribing a refractive index modulation having the grating period variation (z) in an optical fibre, whereby the phase-modulated FBG is operable in transmission to output an output optical signal f.sub.out(t) in response to an input optical pulse f.sub.in(t).

8. A method according to claim 7, wherein calculating the grating period variation (z) for the phase-modulated FBG includes performing an iterative numerical optimisation process to bring a calculated spectral response |H.sub.T()| towards the objective spectral response |H.sub.T,obj()|.

9. A method according to claim 8, wherein the iterative numerical optimisation process includes: obtaining the calculated spectral response |H.sub.T()| from the coupling strength |(z)| and a candidate grating period variation function .sub.i(z), calculating an error between the calculated spectral response |H.sub.T()| and the objective spectral response |H.sub.T,obj()|, and selecting the next candidate grating period variation function .sub.i+1(z) based on the error between the calculated spectral response |H.sub.T()| and the objective spectral response |H.sub.T,obj()|.

10. A method according to claim 7, wherein inscribing the refractive index modulation includes irradiating the optical fibre with ultraviolet radiation through a phase mask that has the grating period variation (z) encoded thereon.

11. A method according to claim 7, wherein the objective impulse response h.sub.T,obj(t) is .sub.n=0.sup.N1.sub.n(tnT), where .sub.n and N are selected to ensure correspondence to a minimum phase function.

12. The method according to claim 7, wherein objective impulse response is selected to correspond to a time-spaced series of two or more optical pulses in response to a single input pulse.

13. A method of fabricating a phase mask for inscribing a phase-modulated fibre Bragg grating (FBG) in an optical fibre, the method comprising: obtaining an objective spectral response |H.sub.T,obj()| that is a Fourier transform of an objective impulse response h.sub.T,obj(t) of the phase-modulated FBG, where the objective impulse response corresponds to a minimum phase system; selecting a coupling strength |(z)| to be exhibited by the phase-modulated FBG along its length z; calculating a grating period variation (z) for the phase-modulated FBG using the objective spectral response |H.sub.T,obj()| and the coupling strength |(z)|; and fabricating a phase mask, whereby the grating period variation (z) is encoded across the phase mask.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Examples of the invention are discussed in detail below with reference to the accompanying drawings, in which:

(2) FIGS. 1A, 1B and 10 are schematic diagrams depicting known MZI configurations;

(3) FIG. 2 is a schematic diagram depicting two embodiments of a delay line interferometer that are embodiments of the invention;

(4) FIGS. 3A, 3B and 3C are graphs depicting objective and simulated spectral response amplitudes and a corresponding grating period variation associated with a delay line interferometer that is a first embodiment of the invention;

(5) FIGS. 4A, 4B and 4C are graphs depicting objective and simulated spectral response amplitudes and a corresponding grating period variation associated with a delay line interferometer that is a second embodiment of the invention;

(6) FIG. 5 is a schematic flow diagram illustrating the a numerical optimisation process for obtaining a grating period variation for use in the present invention.

DETAILED DESCRIPTION; FURTHER OPTIONS AND PREFERENCES

(7) FIGS. 1A, 1B and 1C illustrate various known configurations for MZIs.

(8) FIG. 1A shows a traditional MZI in which an input signal from a source is divided by a beam splitter. The two paths are recombined using mirrors at another beam splitter. The optical path lengths of the two paths are arranged to be slightly different so that a pair of replica input signals is output from the second beam splitter.

(9) FIG. 1B shows a MZI arrangement implemented using a pair of optical fibres extending between two couplers. This arrangement operates in the same way as FIG. 1A, in that the optical path lengths of the two optical fibres between the couplers is arranged to be different, so that an input signal introduced to the optical fibres at the first coupler takes longer to propagate through one of the optical fibres relative to the other, so that the output from the second coupler comprises two time delayed replicas of the input signal.

(10) FIG. 1C is a schematic diagram illustrating a lattice-type MZI structure, where a plurality of MZIs are arranged in a series of stages to generate multiple replicas from an original input signal.

(11) FIG. 2 illustrates schematically two examples of an delay line interferometer which are embodiments of the invention. Instead of physically splitting the input pulse, as in the traditional arrangements discussed above, the invention uses a suitably configured transmissive FBG 10 fabricated within an optical fibre 12 to provide the desired interference functionality.

(12) The optical fibre 12 may be of any conventional type, e.g. made of silica and having a core for supporting propagation of optical radiation surrounded by a cladding layer. The transmissive FBG 10 may be inscribed within the core. The transmissive FBG 10 shown in FIG. 2 is not to scaleit is shown schematically for illustration purposes only.

(13) As shown in FIG. 2, each embodiment has a input portion 14 for receiving input optical radiation. The input optical radiation is in the form of single pulses, e.g. having a Gaussian-like profile, generated by an optical source (not shown). Although the examples use a single pulse as an optical input signal, the present invention can be use with any type of optical input signal from any kind of optical source. For example, the input optical signal may be a digital signal having information encoded therein. However, for the specific example of pulse train generation discussed here, the optical source may for example be a mode-locked laser. Each embodiment also has an output portion 16 for delivered the optical radiation that is transmitted through the transmissive FBG 10, i.e. the optical pulse train. Since each embodiment operates in transmission, there is no need for an optical circulator or other filtering mechanism to extract the output signal.

(14) The embodiment in FIG. 2(a) is arranged to output a pair of time-spaced optical pulses, each being substantially identical to the single input pulse. The embodiment in FIG. 2(b) is arranged to output a train of multiple pulses (four are shown in the drawing). Again, each pulse is substantially identical to the single input pulse.

(15) In each embodiment, the transmissive FBG is a phase-modulated FBG, where the coupling strength remains substantially uniform in the grating. In practice, the phase-modulation profile can be directly encoded on a phase mask, which means the transmissive FBG can be reproduced with very high accuracy. The invention is based on the realisation that a single phase-modulated FBG operating in transmission is very suitable for implementing the function of one or more MZIs, since it can very accurately reproduce the corresponding spectral response.

(16) The theory underlying the invention is now explained. Let us suppose f.sub.in(t) and f.sub.out(t) are the complex envelopes of the input and output of the transmissive FBG respectively, with t as the time variable. Since a transmissive FBG can be considered a linear system, the input and output are related by f.sub.out(t)=f.sub.in(t)h.sub.T(t), where h.sub.T(t) is the impulse response of the transmissive FBG, denotes the convolution operator, and denotes proportionality. The corresponding spectral functions are related by F.sub.out()=F.sub.in()H.sub.T(), where is the base-band angular pulsation, i.e., =.sub.opt.sub.0, where .sub.opt is the optical angular pulsation and .sub.0 is the central angular pulsation of the signals, F.sub.out()=FT[f.sub.out(t)] and F.sub.in()=FT[f.sub.out(t)] are the output and input signal in the spectral domain, and H.sub.T()=FT[h(t)] is the spectral response of the transmissive FBG, where FT[.Math.] denotes the Fourier transform.

(17) To obtain a desired functionality corresponding to N delayed replicas temporally overlapping, an objective impulse response is expressed as h.sub.T,obj(t)=.sub.n=0.sup.N1.sub.n(tnT), whose corresponding spectral response is H.sub.T,obj()=FT[h.sub.T,obj(T)]=.sub.n=0.sup.N.sub.N exp(jnT).

(18) To achieve this functionality in practice, the spectral response of the FBG in transmission must meet H.sub.T()H.sub.T,obj (). In general, we cannot simultaneously impose |H.sub.T()| and H.sub.T(), since they are related by means of the logarithmic Hilbert transform (LHT) [5] in a transmissive FBG. However, both the amplitude and the phase of the spectral response objective, H.sub.T,obj(), can be simultaneously obtained if h.sub.T,obj(t) is a minimum phase function.

(19) The above theory is illustrated by way of the following examples.

(20) As a first example, we consider a single MZI operation. In this example, the desired interference functionality of the phase-modulated FBG corresponds to a selection of N=2, .sub.0=.sub.1= and an interferometer delay T=20 ps in the above formula for the objective impulse response h.sub.T,obj(t). This function is a minimum phase function, since the corresponding system and its inverse are causal and stable.

(21) FIG. 3A is a graph showing an objective spectral response amplitude |H.sub.T,obj()| as a dotted line and a simulated actual spectral response amplitude |H.sub.T()| as a solid line. The objective spectral response amplitude |H.sub.T,obj()| is obtained from the Fourier transform of the objective impulse response h.sub.T,obj(t) The simulated actual spectral response amplitude |H.sub.T()| is obtained from the numerical optimization process discussed below.

(22) FIG. 3B shows the grating period variation (z) and the coupling coefficient |(z)| for a phase-modulated FBG that exhibits the desired interference functionality. The phase-modulated FBG has a length of 9 cm, and the coupling coefficient |(z)| is a raised cosine function with a roll-off factor of 10% and maximum amplitude 258.2 m.sup.1. The grating period variation (z) is obtained from the numerical optimization process discussed below.

(23) FIG. 3C shows the simulated output of the grating in response to a single 5 ps FWHM Gaussian input pulse centred on 1550 nm. It can be seen that the phase-modulated FBG acts to generate a pair of output pulses having the same profile as the input pulse. Clearly, in this example the output is a time-spaced pair of replicas of the input signal. Choosing a longer input signal will cause the time-delayed replicas to interfere with each other.

(24) As a second example, we consider a multiple MZI operation. In this example, the desired interference functionality of the phase-modulated FBG corresponds to a selection of N=4, .sub.0=.sub.1=.sub.2=.sub.3= and an interferometer delay T=20 ps in the above formula for the objective impulse response h.sub.T,obj(t). This function is a minimum phase function, since the corresponding system and its inverse are causal and stable.

(25) FIG. 4A is a graph showing an objective spectral response amplitude |H.sub.T,obj()| as a dotted line and a simulated actual spectral response amplitude |H.sub.T()| as a solid line. The objective spectral response amplitude |H.sub.T,obj()| is obtained from the Fourier transform of the objective impulse response h.sub.T,obj(t). The simulated actual spectral response amplitude |H.sub.T()| is obtained from the numerical optimization process discussed below.

(26) FIG. 4B shows the grating period variation (z) and the coupling coefficient |(z)| for a phase-modulated FBG that exhibits the desired interference functionality. The phase-modulated FBG has a length of 9 cm, and the coupling coefficient |(z)| is a raised cosine function with a roll-off factor of 10% and maximum amplitude 356.8 m.sup.1. The grating period variation (z) is obtained from the numerical optimization process discussed below.

(27) FIG. 4C shows the simulated output of the grating in response to a single 5 ps FWHM Gaussian input pulse centred on 1550 nm. It can be seen that the phase-modulated FBG acts to generate a series of four output pulses having the same profile as the input pulse.

(28) It can be understood that the invention may be implemented with many other examples of desired interference functionality, as long as the corresponding objective impulse responses h.sub.T,obj(t)=.sub.n=0.sup.N1.sub.n(tnT) corresponds to a minimum phase system.

(29) FIG. 5 shows schematically a method for obtaining the grating period variation (z) based on the theory outlined above using a numerical optimisation technique. The technique is similar to a known method of obtaining grating period variation for pulse shaping purposes [6].

(30) In the method shown in FIG. 5, the functions representing the objective spectral response amplitude |H.sub.T,obj()| and the coupling coefficient amplitude |(z)| are provided. Although other restrictions can be specified, they need to be carefully selected, otherwise the search space can be overly reduced, excluding satisfactory solutions. Importantly, unlike the transmissive FBG synthesis algorithm proposed in [5], the phase of the spectral response in reflection is not specified, and hence a conventional inverse scattering algorithm [7] cannot be applied. In this method, a numerical optimization algorithm calculates the grating modulated phase, or equivalently the grating period variation (z), in order to obtain a simulated spectral response in transmission |H.sub.T()| that attempts to better approach the objective spectral response in transmission in terms of least minimum squares over a desired bandwidth.

(31) In practice, an error between the simulated (calculated) spectral response |H.sub.T()| and the objective spectral response |H.sub.T,obj()| is determined and used to influence the selection of the next candidate grating period variation function .sub.i1(z) to be used in simulating the spectral response |H.sub.T()|. The numerical optimisation process is arranged to reduce the error through suitable selection of a profile for the grating period variation.

(32) A delay line interferometer according to the invention may find application in various pulse characterisation techniques, e.g. optical sampling in photonically-assisted ADC implementations, Spectral Phase Interferometry for Direct Electric-Field Reconstruction (SPIDER). Such techniques currently use conventional MZI structure. The invention may enable more compact and lower loss solutions to be obtained. Such temporal interferometry devices can also be used for several digital modulation schemes, e.g. DPSK and DQPSK demodulation (for N=2), as well as for OFDM generation and demodulation (for N>2).

REFERENCES

(33) [1] J. H. Lim, H. S. Jang, Lee, J. C. Kim, and B. H. Lee, Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings, Opt. Lett. 29, 346-348 (2004).

(34) [2] Jiangbing Du, Yongheng Dai, Gordon K. P. Lei, Weijun Tong, and Chester Shu, Photonic crystal fiber based Mach-Zehnder interferometer for DPSK signal demodulation, Opt. Express 18, 7917-7922 (2010)

(35) [3] T. Allsop, R. Reeves, D. J. Webb, I. Bennion, and

(36) R. Neal, A high sensitivity refractometer based upon a long period grating Mach-Zehnder interferometer, Review of scientific instruments, 73, 1702-1705.(2002)

(37) [4] C. R. Liao, Y. Wang, D. N. Wang, and M. W. Yang, Fiber in-lineMach-Zehnder interferometer embedded in FBG for simultaneous refractive index and temperature measurement, IEEE Photon. Technol. Lett., vol. 22, no. 22, pp. 1686-1688, Nov. 15, 2010.

(38) [5] J. Skaar, J. Opt. Soc. Am. A 18, 557-564 (2001).

(39) [6] M. A. Preciado, X. Shu, and K. Sugden, Proposal and design of phase-modulated fiber gratings in transmission for pulse shaping, Opt. Lett. 38, 70-72 (2013).

(40) [7] R. Feced, M. N. Zervas and M. A. Muriel, IEEE Journal of Quantum Electronics, 35, 1105-1115, (1999).