† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11274377 and 61176006) and the State Major Research Equipment Project, China (Grant No. ZDY2011-2).
Propagation of a signal beam in an AlGaAs/GaAs waveguide multiple-prism light deflector is theoretically investigated by solving the scalar Helmholtz equation to obtain the dependences of the temporal and spatial resolvable characteristics of the ultrafast deflector on the material dispersion of GaAs including group velocity dispersion and angular dispersion, interface reflection, and interface scattering of multiple-prism deflector. Furthermore, we experimentally confirm that, in this ultrafast beam deflection device, the deflecting angle of the signal light beam is linear with the pump fluence and the temporal resolution of the ultrafast deflection is 10 ps. Our results show that the improvement of the temporal and spatial resolvable performances is possible by properly choosing the structural parameters and enhancing the quality of the device.
Optical beam deflecting and scanning have found many applications in civil and military systems. The available techniques include mechanical, acousto–optic, electro–optic, all-optical devices and so on.[1–4] Among them, the mechanical deflectors are limited in developing owing to their low deflecting speed. The acousto–optic devices had been most interesting, but their access speed and resolvable power are still not high enough. Although electro–optic deflectors can scan faster comparatively, the relative phase change induced by electro–optic effect is small in most of the electro–optic materials. Thus it requires a long optical path length in these electro–optic crystals, which is limited by the materials themselves.[5] In addition, the driving power for the electro–optic devices is mostly large. The polymeric material has been reported to be a promising candidate instead of the electro–optic crystal, because of its compatibility with different substrates, ease of fabrication, low cost, and not so high driving voltage as the electro–optic material, despite a lack of thermal stability and relatively large insertion losses.[6] Borrowing the method in phased array radar, many phased array optical scanning devices have been implemented.[7,8] However, none of these approaches are ultrafast enough to apply in the ultrafast light signal scanning/steering. The present popular ultrafast travelling-wave electro–optic deflector employs a quasi-velocity-matching technique to compensate the velocity mis-match between an optical group velocity and a microwave phase velocity, which can operate in a picosecond timescale.[9] Furthermore, light deflecting controlled with light is also proposed,[10–12] some of which can easily promote an ultrafast light deflection.
The development of the ultrafast optical deflecting/scanning devices brings an inspiration for the improvement of many optical and photoelectric devices. Take the image converting tube streak camera as an example. The meander-type travelling-wave deflecting plate takes the place of the more conventional standing-wave parallel-plate to acquire both increased deflection sensitivity and frequency bandwidth.[13,14] To proceed, the fact that space charge effect leads to a trade-off between the temporal resolution and dynamic range when the signal energy is high is becoming a serious obstacle for the further performance improvement of this image converting tube streak camera.[15] In the early stages, direct deflecting of the optical beam using an electro–optic deflector had been proposed instead of photoelectron beam scanning manner in the image converting tube streak camera.[16] In the year of 2010, Chris’s group first demonstrated that the serrated light illumination for deflection-encoded recording (SLIDER) concept enables the single shot all-optical solid state camera, which is an example of direct beam scanning.[17] There are plenty of other applications that can benefit from the development of the optical deflecting devices.[18–20]
In our previous work, we have investigated the statically deflecting characteristics of a CW signal laser at the wavelength of 1053 nm passing through a multiple-prism deflector under the illumination by a 800 nm CW pump laser.[21] This work will research an ultrafast beam deflection by arranging the same multiple-prism deflector in the pump probe configuration. Pump probe technique has been successfully and universally applied to investigate the carrier dynamics of the photo-excited materials, where two ultrafast pulses with arbitrary time delay complete the scanning of the dynamic process. By adjusting the time delay between the pump pulse and the probe pulse (denoted as signal pulse in our context), the deflection of the signal light beam can be linearly controlled. The multiple-prism deflector employs an AlGaAs/GaAs waveguide with a serrated gold mask on its surface to realize the discrete deflection of the signal light beam. Study on the transient absorption or transmission of the intrinsic GaAs has shown that the generation of the non-equilibrium free carriers can be recognized as instantaneous as the pulse duration time and their relaxation time can come up to nanosecond scale.[22,23] Therefore, high response speed and high repetition are allowed in this ultrafast deflection device. In the context, Section 2 gives a theoretical study on the dependences of temporal and spatial resolvable performances on the material dispersion of GaAs including group velocity dispersion and angular dispersion, interface reflection, and interface scattering of the deflector. Section 3 demonstrates the experiments about this ultrafast deflection device. The experimental results show that the temporal resolution is about 10 ps, which is not so much satisfying but really promising in the ultrafast signal scanning, optical communication, light controlling and switching.
Figure
The refractive index distribution of a multiple-prism deflector can be expressed as
If the incident light beam is a temporal ultrafast signal, we can resort to Fourier analysis. E0 (x, z, t) is the initial electric field of the ultrafast signal. The Fourier transform of the initial electric field is
The temporal resolution of the ultrafast deflector can be simply defined as tr = T/M. T is the time that the light signal spends passing through the entire length of the deflector and T = L/vs. L is the entire length of the deflector and vs is the group velocity of the ultrafast signal light in the deflector. The number of the resolvable spots of the deflector is obtained by M = θ/δθ, where θ is the deflecting angle and θ = LΔn/a, δθ is the angular resolvability of Gaussian beam and
In the simulation, propagation of the light beam in a multiple-prism deflector surrounded by free space is investigated through solving 2D Helmholtz equation by a finite element method with a given initial field profile. The dimensions of the deflector are a × Ntb, where a = 100 μm, b = 13 μm, and Nt is the total number of prisms. The evaluations of a and b here are the reduced scale of the dimensions of the experimental sample in a proportional ratio of 3:5. The refractive index change Δn is equal to 0.01 (the negative sign is omitted in the context, for it only matters with the deflection direction of the signal beam) according to Bennett’s study. Figure
The initial field of the incident ultrashort pulse is supposed to have a Gaussian expression
The intensity of the output pulse from our laser has a nearly Gaussian distribution with a center wavelength of λ0 = 1 μm and a pulse duration (1/e full width) of 120 fs. Therefore, τ = 85 fs. The spectral 1/e half width of the incident temporal pulse is Δω/2 = 2/τ, accordingly, Δλ = 25 nm (full width).
The material dispersion of GaAs can be given by Sellmeyer formula
Figure
On the other hand, the dependence of material refractive index on the wavelength has two effects on the ultrafast signal pulse propagating in a multiple-prism deflector, one in space termed as angular dispersion (AD) and the other in time termed as group velocity dispersion (GVD). Both can result in the width broadening of the signal pulse. The GVD brings about the group delay dispersion (GDD), while the AD always yields negative group delay dispersion. The temporal resolution of an ultrafast deflector can also be characterized by the broadened width of an ultrashort pulse passing through the deflector. The broadened full width of signal light field Δτ relating to the GDD can be expressed as Δτ = GDD×Δω. The net GDD of the ultrafast signal pulse after propagating the deflector due to AD and GVD can be directly acquired by taking the second derivative of the spectral phase φ (ω) of the deflected signal field with respect to ω, that is
Apart from the effect of material dispersion on the temporal resolution, the structural parameters of the deflector will greatly impact its spatial resolvable and thus the temporal resolvable characteristics. The total deflecting angle of the multiple-prism deflector can be obtained by θ = LΔn/a under the paraxial approximation. It can be seen that the formula to calculate the deflecting angle depends only on the overall dimension of the deflector and is independent of how the deflector is subdivided into individual prisms, on the conditions that the interfaces between adjacent prisms are straight lines and the lines are joined end to end. However, the subdivision style has an impact on the quality of the electric field profile. The electric field profile of the deflection beam at the end face of the deflector is used to investigate the spatial resolvable characteristics of the deflector.
Based on the above analysis, we examine the influences of the structural parameters Δn, Nt, ws, and different subdivision styles on the profiles of the output electric field. Figure
The semiconductor material is fabricated by the molecular beam epitaxy (MBE). The undoped waveguide core is a 0.6-μm-thick layer of GaAs, which is sandwiched between a 2-μm-thick upper cladding layer (Al0.24Ga0.76As) and 3-μm-thick lower cladding layer (Al0.24Ga0.76As) on top of a GaAs substrate. On the waveguide surface, a serrated gold mask is formed by photolithography. The serrated mask is an array of right triangles with two leg lengths of 350 μm and 45 μm, respectively. The number of the triangles Nt is 100. The layering structure of optical deflector is shown in the inset of Fig.
The experimental setup for ultrafast light deflection is shown in Fig.
As shown in Fig.
At the beginning of the experiment, the pump pulse arrives at the upper surface of the deflector when the signal pulse just begins to exit from its end face. In this case, the signal pulse has no deflection. By gradually decreasing the optical path of the pump pulse, the signal pulse will experience an increasing number of prisms and obtain corresponding deflection. At the moment when the signal pulse propagates through the entire prism array, it will obtain a maximum deflection. Out from the deflector, the deflected signal is focused and coupled onto a CCD camera for recording.
The group refractive index corresponding to the ultrashort signal pulse with a center wavelength of 1000 nm is denoted as ns. In GaAs, ns = 3.8. Therefore, T = 57 ps for the deflector sample. Figure
Figure
As shown in Figs.
Figure
Figure
Here, we omit the time jitter of laser pulses, for the achieved temporal resolution of 10 ps is much larger than the jitter of femtosecond scale. Theoretical temporal resolution of the deflector can be calculated to be 4.2 ps with Δn = 0.016. With T = 57 ps, the theoretical result about the number of the resolvable spots of the deflector M = 13.6. However, the achieved experimental temporal resolution is 10 ps. In other words, we can only distinguish five signal light streaks and M ≈ 5 in the experiment. In addition to the reasons discussed in Section 2.2, the temporal resolution depends on many other factors such as the quality of the waveguide, the quality of the smoothness of two end faces of the deflector, non-uniform spatial distribution of pump intensity, the beginning synchronization error between the signal pulse and pump pulse, the imperfect prism array, and so on.
We have demonstrated an ultrafast beam deflection system with picosecond, even to sub-picosecond, temporal resolution, a large number of the resolvable spots, high response and repetition speed. The theoretical investigations show that material dispersion of GaAs including group velocity dispersion and angular dispersion, interface reflection, and interface scattering of the deflector, impose harmful influences on the temporal and spatial resolvable performances. Thus by properly designing the structural parameters of the deflector, a sub-picosecond scale of temporal resolution can be achieved. The experimental results show that the temporal resolution is about 10 ps, which is not very satisfying but can be improved a lot as the theoretical discussion section has suggested. In fact, we can choose proper semiconductor materials of waveguide deflector depending on the wavelength of the signal light to be deflected. For example, AlGaAs/GaAs is the proper choice for the near infrared signal light with wavelength larger than 870 nm, whose photon energy does not fall into the absorption range of the waveguide core. In the same way, the use of a wider bandgap semiconductor for the waveguide core would enable operation well into the visible spectrum, such as AlmGa1 −mAs with a proper value of m. If m = 0.37 and then λg = 650 nm, the signal light wavelength can be larger than 650 nm. Except for the all-optical solid-state streak camera, this configuration can also be used in the optical communication, light controlling and switching, and so on.
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