Section #6
x.xx High Repetition Rate Generation of Arbitrary Lightwave and Millimeter-wave Signals
Jason D. McKinney, Prof. Dongsun Seo, and Prof. Andrew M. Weiner
Supported by the Army Research Office, the National Science Foundation, and Intel Corporation
Key words: pulse shaping; ultrafast optics; lightwave communications; photonics; mm-waves; rf photonics
This research involves generation of arbitrarily shaped high-speed waveforms: both ultrafast optical waveforms in the 1550 nm lightwave communications band and ultrawideband electromagnetic waveforms in the mm-wave band.
In the optical thrust of our work, we have performed research on a direct space-to-time (DST) pulse shaper, in which the output ultrafast optical waveform or pulse sequence is a direct temporal replica of a spatial masking pattern [1].
This direct scaling relationship is advantageous for applications in ultrafast parallel-to-serial conversion. In previous work we constructed the first DST pulse shaper that works in the 1550 nm lightwave communications band [2].
During the last year, we have read-out the DST shaper using a new ultrashort pulse fiber laser source that provides pulses with durations below 400 fsec at 10 GHz repetition rate. As a result, we are now able to generate continuously periodic, modulated 100 GHz optical pulse sequences [3]. This result is a substantial step forward towards practical application.
We have also obtained significant new results by applying our pulse shaper for millimeter-wave arbitrary waveform generation. We have previously demonstrated that our direct space-to-time technology can be exploited in conjunction with a fast (60 GHz bandwidth) optical-to-electronic converter for experiments on generation of burst arbitrary millimeter wave signals [2]. In this way, we leveraged our prowess in optical pulse shaping in order to realize new capabilities for cycle-by-cycle synthesis of extremely wideband electromagnetic waveforms at frequencies in the millimeter-wave regime. During the past year, we took advantage of our new 10 GHz laser source to repeat our arbitrary millimeter wave generation experiments at much higher repetition rates [4]. This results in the first cycle-by-cycle generation of continuous, periodic, ultrawideband signals in the millimeter-wave regime (our previous work demonstrated only burst ultrawideband signals). These results provide for generation of user defined, broadband electromagnetic signals at frequencies more than an order beyond the fastest commercial electronic arbitrary waveform generation instrumentation and may open new opportunities for electronic countermeasures, pulsed radar, and ultrawideband (UWB) wireless communications at millimeter wave frequencies.
References
[1] D.E. Leaird and A.M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quant. Electron. Vol.
37, 2001, pp. 494.
[2] J.D. McKinney, D.E. Leaird, and A.M. Weiner, “Millimeter Arbitrary Waveform Generation with a Direct
Space-to-Time Pulse Shaper,” Opt. Lett. Vol. 27, 2002, pp. 1345.
[3] J.D. McKinney and A.M. Weiner, “100 Gb/s Optical Word Generation Using a 1.5  m Direct Space-to-Time
Pulse Shaper,” Conference on Lasers and Electro-optics, Baltimore, MD, June 2-6, 2003.
[4] J.D. McKinney, D.S., and A.M. Weiner, “Photonically Assisted Generation of Continuous Arbitrary Millimeter
Electromagnetic Waveforms,” Electron. Lett. Vol. 39, 2003, pp. 309.

Caption: Examples of continuous periodic optical data words at 100 Gb/s (left) and continuous periodic millimeterwave voltage waveforms obtained after optical to electronic conversion (right)

x.xx Ultrafast Optical Pulse Sequence Generation Using Integrated Optics
Dr. Daniel E. Leaird and Prof. Andrew M. Weiner
Supported by the Army Research Office, the National Science Foundation, and the Optoelectronics
Industry Development Association (OIDA) through the Joint Optoelectronics Project (JOP)
Key words: ultrafast optics; lightwave communications; photonics; integrated optics; optical signal processng
Due to increasing bandwidth demand for lightwave communications and networking, significant research effort has been devoted to the development of high repetition rate optical pulse sources. Recently we demonstrated a new scheme utilizing an integrated optic component, known as an arrayed waveguide grating (AWG), to generate a high repetition rate burst of short pulses or, in principle, a continuous train at multiple, spatially separated, output wavelengths from a single, lower rep rate femtosecond pulse source [1,2,3]. Although AWGs are commonly used for demultiplexors and routers in wavelength-division multiplexed (WDM) optical communications, our work is the first to reveal that they can also function as a high-rate pulse generator for time-domain networking applications.
In current work [4] we have demonstrated more general femtosecond pulse sequence generation using a modified arrayed waveguide grating (AWG) that provides directly optical access to the waveguide array region. This allows external control of the light coupled into each of the waveguides, which means that data can now be programmed onto the generated optical pulse sequence. This is contrast to our previous experiments on pulse sequence generation using AWGs, where the pulse sequence was fixed. In our experiments to date, waveguide excitation (hence output pulse sequence) has been controlled using prefabricated optical masks. In future implementations the spatially patterned mask could be replaced with an optoelectronic modulator array to permit control of the temporal output pulse profile at subnanosecond frame rates.
References
[1] D.E. Leaird, S. Shen, A.M. Weiner, A. Sugita, S. Kamei, M. Ishii, and K. Okamoto, "Generation of High
Repetition Rate WDM Pulse Trains from an Arrayed-Waveguide Grating," IEEE Photonics Letters, Vol. 13,
2001, pp. 221-223.
[2] D.E. Leaird and A.M. Weiner, "Direct Space-to-Time Pulse Shaper and Optical Pulse Train Generation," U.S. patent #6,577,782, issued June 10, 2003.
[3] D.E. Leaird, A.M. Weiner, S. Kamei, M. Ishii, A. Sugita, and K. Okamoto, “Generation of Flat-Topped 500
GHz Pulse Bursts Using Loss Engineered Arrayed Waveguide Gratings,” IEEE Photon. Tech Lett. Vol. 14,
2002, pp. 816-818.
[4] D.E. Leaird and A.M. Weiner, “High Repetition Rate Direct Space-to-Time Pulse Shaping Using a Modified
Arrayed Waveguide Grating,” Conference on Lasers and Electro-optics, Baltimore, MD, June 2-6, 2003.
Caption: Modified arrayed waveguide grating schematic (left) and generated ultrafast optical pulse sequence (right)

x.xx Compensation and sensing of polarization-mode dispersion
Mehmet Akbulut, Ryan Nelson, Xiang Wang, and Prof. Andrew M. Weiner
Supported by the National Science Foundation and the Purdue University Trask Fund; performed in collaboration with CRI, Inc.
Key words: lightwave communications; photonics; polarization-mode dispersion; optical signal processing; ultrafast optics; pulse shaping
Polarization mode dispersion (PMD) is a major issue in high-speed optical fiber communications, especially at bit rates of 40 Gb/s and above [1]. Arising from small random birefringences in fibers, this effect leads to complicated wavelength-dependent polarization scrambling and polarization- and wavelength-dependent delays. The result is to degrade error rates in optical communications. Our goal in this research project is to exploit and extend technology developed in the field of ultrafast optical pulse shaping [2] to compensate PMD of wide-band optical signals in parallel on a wavelength-by-wavelength basis and under computer control. This improves on current approaches that only allow compensation of so-called first order PMD for a single wavelength and which do not apply to situations with wide-band optical signals where the distortion caused by PMD varies substantially across the optical bandwidth.
As a first step in our research project, we have achieved results on sensing and compensation of wavelengthdependent polarization scrambling, summarized as follows:
 We have demonstrated the world’s first wavelength-parallel polarization sensor
[3], which can measure the complete state-of-polarization of 256 wavelength components in parallel in under 1 millisecond, which yields an overall sensing rate 100 times faster than conventional, single-channeled commercial polarimeters.
Our sensor should be fast enough to be used in a feedback control loop for PMD compensation.

By using a novel liquid crystal modulator array geometry (obtained through collaboration with CRI, Inc.), we have for the first time demonstrated the use of an optical pulse shaper for wavelength-by-wavelength polarization compensation. In particular, we are able to take an input field with strongly wavelengthdependent polarization and restore it to a nearly wavelength-independent linear polarization [4]. This can significantly reduce penalties associated with polarization-dependent loss of optical components.
References
[1] C.D. Poole and J. Nagel, Polarization Effects in Lightwave Systems , in Optical Fiber Telecommunications ,
I.P. Kaminow and T.L. Koch, Editors. 1997, Academic Press: San Diego.
[2] A.M. Weiner, "Femtosecond Pulse Shaping Using Spatial Light Modulators," Rev. Sci. Instr. Vol. 71,
2000, pp. 1929-1960.
[3] X. Wang, and A. M. Weiner, “Fast Wavelength-Parallel Polarization Sensor for Multi-Wavelength Optical
Networks,” Conference on Lasers and Electro-optics, Baltimore, MD, June 2-6, 2003.
[4] M. Akbulut, R. Nelson, A. M. Weiner, P. Cronin, and P. J. Miller, “Programmable Multi-Wavelength
Polarization Corrector,” Conference on Lasers and Electro-optics, Baltimore, MD, June 2-6, 2003.

Caption: Transmission of broadband optical field through a polarizer, either with wavelength-dependent polarization or after polarization correction. Polarization-dependent loss is reduced by 12 dB. x.xx Generalized Theory of Optical Second Harmonic Generation Efficiency
Haifeng Wang, and Prof. Andrew M. Weiner
Supported by the National Science Foundation
Key word: nonlinear optics; photonics; ultrafast optics; second harmonic generation
Second harmonic generation (SHG), also known as frequency doubling, is is a textbook example of nonlinear optics. SHG provides a simple way to generate coherent light at wavelengths near 400nm or below, which is attractive for numerous applications including optical data storage, optical printing, visual displays, photolithography, and medical uses. It is also widely used in measurement of ultrafast optical pulses. High conversion efficiency is usually preferred. There are two major ways to increase SHG efficiency for a specified nonlinear material: increase input intensity and increase crystal length. The former invokes the need for pulsed laser sources and beam focusing; the latter increases the significance of temporal and spatial walk-off effects, in which the second harmonic field separates temporally and spatially from the input field. We have now developed the first analytic first theory which can predict efficiency in the case of simultaneous temporal and spatial walk-off [1,2].
This generalizes on previous theories, which included focusing and spatial walk-off for continuous wave sources [3], or focusing and temporal walk-off for pulsed sources without spatial walk-off [4]. Also, these previous theories
[3,4] are restricted to the case of low conversion efficiency, for which the input field remains constant; our theory is valid at least approximately well into the regime where the input field is significantly depleted. We have also performed a series of experiments which support the validity of our theory [1,2]. Our theory provides an effective tool to predict SHG efficiency under conditions not previously described via an analytical formulation and provides new insight into the SHG conversion process itself.
References
[1] H. Wang and AM. Weiner, “Second Harmonic Generation Efficiency with Simultaneous Temporal Walkoff,
Spatial Walkoff, and Depletion,” Conference on Lasers and Electro-optics, Baltimore, MD, June 2-6, 2003.
[2] H. Wang and AM. Weiner, “Efficiency of Short Pulse Type I Second Harmonic Generation with Simultaneous
Spatial Walk-off, Temporal Walk-off and Pump Depletion,” IEEE Journal of Quantum Electronics, in press.
[3] G. D. Boyd, D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams”, Journal of Applied
Physics, Vol. 39, 1968, pp. 3597.
[4] A.M. Kan’an, D. E. Leaird and A. M. Weiner, “High Efficiency Blue Generation by Frequency Doubling of
Femtosecond Pulses in a Thick Nonlinear Crystal”, Opt. Lett. Vol. 23, 1998, pp. 1441-1443.