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We demonstrate a pulse-shaping technique that allows for spectrally resolved splitting of an input signal to multiple output ports. This ability enables reconfigurable creation of splitters with complex wavelength-dependent splitting ratios, giving similar flexibility to a Field Programmable Gate Array (FPGA) in electronics. Our technique can be used to create reprogrammable optical (interferometric) circuits, by emulating their multi-port spectral transfer functions instead of the traditional method of creating an interferometer by splitting and recombining the light with an added delay. We demonstrate the capabilities of this technique by creating a Mach-Zehnder interferometer, an all-optical discrete Fourier transform filter, two nested Mach-Zehnder interferometers and a complex splitter with a triangular-shaped response.
© 2013 Optical Society of America
1. Introduction
Spectral pulse shapers (SPSs) are extremely flexible, reconfigurable spectral filters for phase and intensity manipulation [1–3]. Their high degree of control over the light field has enabled applications in many different areas of science and engineering. In chemistry and biology, researchers have taken advantage of the phase and amplitude manipulation capability to shape the spectrum of incoming femtosecond light pulses, e.g. from a mode-locked laser, into a desired output, to excite specific molecular transitions or increase the resolution of nonlinear spectroscopy [4, 5]. In telecommunications, SPSs have been and are being used as switching devices and for flexible dispersion compensation [6, 7].
While some platforms offer the ability to direct different wavelength components to one of several output fibers, which forms the basis of so-called wavelength selective switches (WSSs) for optical routing in telecommunications networks [6], they do not provide the ability to split light of a single wavelength into multiple output ports.
Previous work has shown, that light of the same wavelength component can be split to multiple output locations (i.e Frisken et al.[8] showed that a fixed portion of light of a wavelength channel can be split to a separate port to implement a drop-and-continue function for a WSS, and Vaughan et al.[9] showed spectral and spatial shaping with a free space output). Here we significantly extend spectral pulse shaping to fully take advantage of these splitting capabilities to create devices with variable, wavelength-dependent splitting of light to multiple outputs. This enables the creation of filters with multi-output spectral transfer functions and thus the ability to implement complex wavelength-dependent splitters and interferometers, including nested interferometer structures.
In this paper we implement, for the first time, a SPS that uses computer generated hologram (CGH) techniques to split light of a spectral component into multiple output ports, while retaining the phase and intensity manipulation capabilities of traditional SPSs. The splitting ratio can be varied as a function of wavelength and we therefore create an versatile reconfigurable emulator for complex structures with overlapping multi-output transfer functions such as interferometers or interferometric circuits. In contrast to a traditional SPS, which can also emulate a single output of an interferometer [10], our device can emulate structures and optical circuits with up to four simultaneous outputs. Such structures are becoming increasingly important in optical communications as networks move to use phase and intensity modulation formats such as quadrature phase-shift keying (QPSK), and advanced multiplexing schemes with (partially) overlapping spectra such as orthogonal frequency division multiplexing (OFDM). With this degree of reprogrammabilty, we can begin to envisage reconfigurable optical circuits that offer the flexibility of reconfigurable electronic circuits (Field Programmable Gate Array – FPGA), albeit in the analog optical domain.
To verify the device capabilities, we created four multi-output filters. A Mach-Zehnder interferometer (MZI) demonstrates the ability to combine the splitting with other SPS functionality. An all-optical discrete Fourier Transform (DFT) filter, which enables demultiplexing of optical OFDM signals [11], and a circuit of two nested interferometers establish the splitting to four ports simultaneously. A two-way splitter with a ratio that varies triangularly with optical frequency demonstrates that our technique allows emulation of complicated structures that do not have an intuitive free-space interferometric equivalent.
2. Principle
In contrast to traditional SPSs based on a spherically symmetric 4-f system in transmission, our device uses a reflective liquid crystal on silicon (LCOS)-based spatial light modulator (SLM). A schematic of the operation principle and a top view of the device layout is depicted in Fig. 1. The optical layout of the device is the same as the one introduced in [6] and [12]. However, this device is currently not able to split light of the same wavelength component along several output ports. Here we extend its functionality to split single wavelength component light into multiple output ports, by CGH-based techniques for creating phase masks on the LCOS. The device is based on a 4-f imaging system – only in the dispersive axis – in reflection, with the LCOS SLM acting as a reflective spatial phase modulator capable of modifying the wavefront of the reflected light orthogonal to the dispersive axis. Light from an input-output fiber array passes through polarisation diversity optics based on a highly birefringent crystal. The polarisation optics spatially separate and align the orthogonal polarisation states to the highly efficient s-polarisation of the diffraction grating. The input light is then reflected off the imaging mirror onto the grating at near Littrow incidence, which angularly disperses the light onto the LCOS array, such that the different wavelength components are spread out over its horizontal axis. The spectral bandwidth of our device is the C-band. Diffraction in the vertical direction causes an approximately Gaussian intensity distribution along the vertical axis of the LCOS. Upon reflection from the LCOS the path of the light is retraced back to the imaging mirror at an angle determined by the beam-steering phase-image applied to the LCOS display. The angular dispersion of the spectral components is subsequently undone by a second pass over the grating before the light is coupled to one of the four output fibers. The Optical Transfer Function (OTF), a measure of the overall optical resolution, of the device is approximately 10 GHz, with a pixel resolution of 4.5 GHz/pixel.
Fig. 1 (a) Principle of the SPS with multiport splitting (LCOS: greyscale presentation of LCOS phase image for creating a MZI). (b) Top view of the actual device layout illustrating the optical path for the two orthogonal polarisations (GRISM: Grating Prism).
The LCOS device acts as a spatial phase modulator, which enables extensive phase and amplitude filtering operations. For this the desired phase is mapped onto the LCOS by a modulus 2π operation and a pre-calibrated conversion into an 8 bit pixel value. A vertical phase modulation (i.e. a phase ramp φ = m · y, where y is the vertical dimension of the LCOS) along a pixel-column of the LCOS will vertically deflect the light to a specific output fiber. Note that although the LCOS only modulates the spatial phase, attenuation of a spectral component is possible by misaligning from the ideal output coupling condition. Similarly, phase control along the horizontal axis of the LCOS enables phase manipulation of the spectral components of the incoming light. Bandpass filtering is implemented by simply using different horizontal regions of the LCOS (see [12] for a more detailed discussion of the attenuation and phase control capabilities).
Our novel splitting approach is enabled by generating a superposition of phase patterns using a computer generated holography (CGH) approach along the vertical axis of the LCOS device. It is related to methods described in [13] and [14] to obtain phase and amplitude control from a phase-only spatial light modulator. Our technique is based on the superposition of the phase profiles that couple to the individual output ports. This superposition is weighted by the splitting ratio between the ports to achieve the desired power distribution over the ports. Therefore, given the vertical phase profiles φ1, φ2 ... that couple all the light to output ports 1, 2 . . . respectively, the combined phase profile that splits the light amongst these output ports becomes:
where the individual phase profiles are vertical phase ramps φi(y) = mi · y, y is the vertical dimension of the LCOS, A is the intensity distribution along this axis, which in general can be considered Gaussian shaped, Arg denotes the complex argument, i.e. the phase. Ci(λ) and ϕi(λ) are factors which determine the wavelength dependent splitting ratio and spectral phase respectively.Figure 2 further illustrates the method of splitting light of a single wavelength component into two output ports. The top row of the figure depicts the intensity distribution along the vertical axis of the LCOS for a single wavelength component. The bottom row illustrates the intensity distribution at the output coupling plane of the device, with the two semi-circles indicating the positions of two output fibers. The intensity distribution is approximately Gaussian as the spatial distribution of the light from the input fiber is imaged onto the LCOS. By imposing a spatial phase retardation with the LCOS (indicated by the black line, and modulus 2π by the red line) the light is spatially displaced to couple into either of the two output fibers (b1 and b2). A LCOS phase corresponding to a superposition of the two profiles in (a1) and (a2) as seen in (a3), results in a intensity distribution with light being equally split between outputs 1 and 2 (b3). Because an LCOS is a spatial phase modulator only, we see that the superposition of the two phase profiles causes higher-order diffraction. This diffraction causes additional loss, which is dependent on the number of output ports and the splitting ratio. This loss is at maximum when light is split into all ports equally and is approximately 0.75 dB for two and 2.2 dB for four simultaneous output ports.
Fig. 2 (a) Spatial intensity distribution of a single wavelength component at the LCOS (blue) and phase profile imposed by the LCOS (black, red (wrapped modulus 2π)). (b) Spatial intensity distribution at the fiber array plane of the SPS. The red and green dots indicate the positions of two output fibers (other fibers omitted for clarity). (1) Light directed to output 1, (2) light directed to output 2, (3) equal splitting of light between output 1 and 2.
The splitting can be performed for individual pixel-columns of the LCOS-array, thus we can choose different splitting ratios for the different wavelength components of the incoming light-field. Furthermore, traditional wavelength selective phase and attenuation control of the SPS is retained by varying Ci and ϕi along the horizontal (wavelength) axis of the LCOS. This allows us to define wavelength-dependent splitting to multiple output ports. To fully exploit this functionality, it is necessary to eliminate the power variation due to the splitting ratio to keep the overall output power constant. This is achieved by directing part of the light to an in-device dump-location, resulting in a small additional loss. In practice, we therefore apply a minimization technique to calculate the correct LCOS image. In the following we will describe the algorithm for the case of splitting into two output ports, it is straightforward to extend it to more outputs.
For any pixel-column of the LCOS, i.e. any wavelength component of the input light, there will be two desired output power ratios R1 and R2 defined as R1 = P1/Ptotal and R2 = P2/Ptotal, where P1,2 is the desired power at port 1 and 2 and Ptotal is the total power. The goal is then to find a phase profile that yields an normalized intensity distribution at the output fiber array such that
where I(y1,2) is the normalized intensity at the position of the two output fibers and Ldiffraction is the additional loss due to higher-order diffraction when light is split at a 50/50 ratio between the two ports. In order to calculate the required phase profile we perform a numerical optimization using a truncated Newton algorithm [15] to find C1, C2 and Cd in Eq. 1 (for three-way splitting), with φ1, φ2 and φd being the phase profiles that direct to Port 1, 2 and the dump port, such that Eq. 3–4 are minimized. Thus in every step of the minimization a phase profile is calculated according to Eq. 1, the output plane of the device is calculated via a Fourier Transform and the error is evaluated according to Eq. 3–4. The procedure is repeated for every pixelcolumn of the LCOS to create the wavelength-dependent splitting profile.This wavelength-dependent splitting capability enables the reconfigurable implementation of multi-output optical circuits via calculating and emulating their respective transfer functions.
3. Experiment
To demonstrate the device capabilities we implemented four complex filters: a 43-GHz FSR MZI, a three-port all-optical DFT filter comprised of three sinc-shaped filters orthogonally spaced at 15 GHz and a fourth continue port (such a device can act as an all-optical demultiplexer for optical OFDM signals in future communication networks [16, 17]), two nested 40-GHz FSR interferometers with a 90° relative phase-shift (DQPSK demodulator), and to demonstrate the capability to create structures without a straightforward interferometer equivalent, a two-port splitter with the splitting ratio varying as a triangular function of optical frequency.
While a delay line MZI is typically implemented by splitting the input light into two paths and recombining the two paths after they have acquired a relative time delay, we take a spectral approach to the design of the interferometer by calculating and emulating the spectral transfer functions of the two MZI outputs simultaneously. The spectral transfer function of the constructive and destructive ports of the MZI are cosine and sine functions of frequency, with the free spectral range (FSR) of the interferometer given by the delay. It can be easily seen that the overall power, i.e. the sum of the powers from both outputs, is constant. The wavelength resolved splitting capability of our SPS device enables us to split the power of the input light into two ports, with a ratio that varies as a function of wavelength (frequency). By implementing this power splitting according to the square of the aforementioned cosine and sine functions and using the phase control to create the appropriate π-phase shifts, we can create both outputs of the MZI interferometer.
The device operation of the MZI was confirmed by measuring the filter response using a commercial optical vector analyzer (Luna OVA 5000), which allows for measurement of phase-response and insertion loss as a function of wavelength for any device-under-test. Figure 3(a) depicts the measured insertion loss and phase response as a function of relative frequency of the constructive and destructive port of the MZI. The center frequency corresponds to a wavelength of 1541.27 nm. For comparison we have added the theoretical insertion loss of the destructive port i.e. a sine wave. We observe excellent agreement. The reduced extinction ratio can be attributed to a combination of limitations in our measurement system and the fundamental limits of our device, however it still remains very good at > 20 dB. Note, that the phase control is crucial for obtaining such a high extinction ratio, as amplitude only control would result in a much reduced attenuation at the null, due to the limited resolution of the device.
Fig. 3 (a) Transfer function of a 43-GHz FSR MZI filter: (solid black) insertion loss of constructive port, (dashed red) insertion loss of destructive port, (dotted black) phase response of constructive port, (dotted blue) theoretical insertion loss of destructive port. (b) Insertion loss of the four output ports of a DQPSK demodulator (solid black, dashed blue, dash-dot green, solid red), (dotted black) phase response of the first port. The theoretical response has been omitted for clarity. The single channel response should match the MZI filter single channel response.
Similarly to the delay line MZI, one can create a DQPSK demodulator, by splitting the light into four output ports. Because the DQPSK demodulator corresponds to two nested MZI interferometers with a 90° relative phase-shift, the transfer functions of the output ports are given by four sinusoids with a 45° phase-shift between them. The measured insertion loss of the four ports and phase response of one of the ports are depicted in Fig. 3(b). Here we have omitted the theoretical curves for clarity reasons, however the single channel response should again match the single channel response of the MZI. The DQPSK demodulator transfer functions deviate slightly stronger from the theoretical sinusoids, due to inaccuracies in the four-way splitting, however better calibration and numerical optimization should result in significant improvements. We also observe a slightly higher overall insertion loss of about 2 dB due to the higher diffraction-based losses mentioned in the previous section.
The ability for generating more complicated circuits is demonstrated by creating an all-optical DFT filter. It is implemented by creating sinc-shaped transfer functions with the maximum of one channel (at one output port) aligning with the nulls of all other channels (at the other output ports) [16]. Here we implemented three channels at a frequency spacing of 15 GHz with all the remaining light directed to a fourth continue channel (not shown). The measured insertion loss of all three channels and phase response of one of the channels is depicted in Fig. 4(a). The center frequency corresponds to a wavelength of 1547.55 nm. Similar to the DQPSK demodulator there is some deviation from the expected theoretical curve due to the four-way splitting, in particular at very high insertion losses. However, this does not impair the operation of the filter for OFDM demultiplexing and multiplexing experiments [11, 18]
Fig. 4 (a) Insertion loss of the three drop ports (solid black, dashed red, dash-dot green) of an all-optical DFT filter, (dotted black) phase response of the first (solid black) drop port, (dotted blue) theoretical response of the second (dashed red) drop port. The fourth, continue port has been omitted for clarity. (b) Normalized linear insertion loss of the two outputs of a splitter with triangular variation of splitting ratio (black, dashed red), (dotted blue) theoretical response.
Finally, our approach enables the easy implementation of devices with a transfer function that does not have an intuitive equivalent circuit in free-space or fibre optics. This is demonstrated by implementing a two-way splitter with a repetitive splitting ratio between the two ports that varies linearly with wavelength, thus forming a triangular transfer function [Fig. 4(b)]. Again the measured insertion loss closely matches the expected behaviour.
Note again, that in contrast to a traditional SPS, which could emulate a single output port of these filters, our device directs light with the desired filter profiles to all output ports simultaneously.
4. Conclusion
In conclusion, we have demonstrated a novel SPS device with software programmable user-defined splitting of single spectral components to the four output ports of the device. This unique capability enables the creation of filters with multi-output overlapping spectral transfer functions, such as present in interferometers or nested interferometer circuits. The device capabilities were shown by implementing a MZI, an all-optical DFT filter, a circuit of two nested MZI interferometers, and a two-way splitter with the splitting ratio varying triangularly with wavelength. The novelty of our approach is the ability to observe all output ports of the filters simultaneously, i.e. the cross and bar (constructive and destructive) port of the MZI and all four output ports of the optical DFT filter. This approach enables rapid prototyping of demodulators, demultiplexers and other complex interferometric filters and splitters, while offering increased stability. Our SPS therefore becomes the optical analog equivalent to an FPGA in electronics, an extremely flexible, reprogrammable optical signal processing device. In addition to the extreme flexibility of our approach, it also offers significant stability, while small length fluctuations in a traditional interferometer can cause a π-phase shift between its two arms and cause a change from constructive to destructive interference, we did not observe variations between constructive and destructive interference over several hour periods.
Acknowledgments
This research was conducted by the Australian Research Council Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (project number CE110001018). This work is also supported under the Australian Research Council’s Discovery and Linkage funding schemes ( DP 1096782, LP0989752). Jochen Schröder likes to also acknowledge his Discovery Early Career Researcher Award (DE120101329), and Benjamin Eggleton his ARC Federation Fellowship (FF0776056).
References and links
1. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000). [CrossRef]
2. V. R. Supradeepa, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: towards higher complexity optical waveforms.” Opt. Express 16, 11878–87 (2008). [CrossRef] [PubMed]
3. S. Vidal, J. Degert, J. Oberlé, and E. Freysz, “Femtosecond optical pulse shaping for tunable terahertz pulse generation,” J. Opt. Soc. Am. B 27, 1044–1050 (2010). [CrossRef]
4. T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001). [CrossRef] [PubMed]
5. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512–514 (2002). [CrossRef] [PubMed]
6. G. Baxter, S. Frisken, D. Abakoumov, H. Zhou, I. Clarke, A. Bartos, and S. Poole, “Highly Programmable Wavelength Selective Switch Based on Liquid Crystal on Silicon Switching Elements,” in “Optical Fiber Communication Conference Engineers Conference,” (Optical Society of America, 2006), paper OTuF2.
7. G.-H. Lee, S. Xiao, and A. Weiner, “Optical Dispersion Compensator With 4000-ps/nm Tuning Range Using a Virtually Imaged Phased Array (VIPA) and Spatial Light Modulator (SLM),” IEEE Photonic Tech. Lett. 18, 1819–1821 (2006). [CrossRef]
8. S. J. Frisken, H. Zhou, D. Abakoumov, G. Baxter, S. Poole, H. Ereifej, and P. Hallemeier, “High performance ’Drop and Continue’ Functionality in a Wavelength Selective Switch,” in “Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference,” (Optical Society of America, 2006), paper PDP14.
9. J. C. Vaughan, T. Feurer, and K. A. Nelson, “Automated spatiotemporal diffraction of ultrashort laser pulses,” Opt. Lett. 28, 2408–2410 (2003). [CrossRef] [PubMed]
10. J. Schröder, O. Brasier, T. D. Vo, M. A. F. Roelens, S. Frisken, and B. J. Eggleton, “Simultaneous multi-channel OSNR monitoring with a wavelength selective switch,” Opt. Express 18, 22299–22304 (2010). [CrossRef] [PubMed]
11. J. Schröder, L. B. Du, M. A. Roelens, B. J. Eggleton, and A. J. Lowery, “Reconfigurable all-optical Discrete Fourier Transform in a Wavelength Selective Switch for Optical OFDM demultiplexing,” in “Optical Fiber Communication Conference (OFC),” (Optical Society of America2012), paper OTh1G.6.
12. M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lightwave Technol. 26, 73–78 (2008). [CrossRef]
13. E. Frumker and Y. Silverberg, “Phase and amplitude pulse shaping with two-dimensional phase-only spatial light modulators,”, J. Opt. Soc. Am. B 24, 2940–2947 (2007). [CrossRef]
14. J. W. Wilson, P. Schlup, and R. A. Bartels, “Ultrafast phase and amplitude pulse shaping with a single, one-dimensional, high-resolution phase mask.,” Opt. Express 15, 8979–87 (2007). [CrossRef] [PubMed]
15. S. Wright and J. Nocedal, “Numerical Optimization” (2006).
16. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing.” Opt. Express 18, 9324–40 (2010). [CrossRef] [PubMed]
17. A. J. Lowery, “Design of Arrayed-Waveguide Grating Routers for use as optical OFDM demultiplexers.” Opt. Express 18, 14129–43 (2010). [CrossRef] [PubMed]
18. L. B. Du, J. Schröder, B. J. Eggleton, and A. J. Lowery, “Reconfigurable optical OFDM transmitter using an inverse optical Fourier transform.” in “Opto-Electronics and Communications Conference (OECC),” (2012), paper PDP1-1.
