All-optical retro-modulation for free-space optical communication.

This work presents device and system architectures for free-space optical and optical wireless communication at high data rates over multidirectional links. This is particularly important for all-optical networks, with high data rates, low latencies, and network protocol transparency, and for asymmetrical networks, with multidirectional links from one transceiver to multiple distributed transceivers. These two goals can be met by implementing a passive uplink via all-optical retro-modulation (AORM), which harnesses the optical power from an active downlink to form a passive uplink through retroreflection. The retroreflected optical power is modulated all-optically to ideally achieve terabit-per-second data rates. The proposed AORM architecture, for passive uplinks, uses high-refractive-index S-LAH79 hemispheres to realize effective retroreflection and an interior semiconductor thin film of CuO nanocrystals to realize ultrafast all-optical modulation on a timescale of approximately 770 fs. The AORM architecture is fabricated and tested, and ultimately shown to be capable of enabling multidirectional free-space optical communication with terabit-per-second aggregate data rates.


Introduction
Free-space optical (FSO) communication and optical wireless communication (OWC) have the potential to enable high-speed networks, providing low latencies and network protocol transparency. Operation with optical carrier frequencies as an alternative to radio frequencies (RF) has major advantages, such as terabit-per-second data rates, no spectrum licensing, improved channel security, reduced power consumption, low system mass, and a greatly reduced antenna diameter [1,2]. These attributes make FSO and OWC technology ideal for future all-optical networks, which have been proposed to circumvent electronic bottlenecks and allow for further network transparency and higher data rates [3]. Applications include military surveillance and reconnaissance, for disseminating large volumes of secure information between many remote locations, as well as providing "last-mile" high-speed telecommunication service in metro or rural areas [4]. However, the major challenge for FSO and OWC bidirectional links is the requirement for line-of-sight alignment with sub-microradian accuracy between transceivers (TRXs) [2]. This is a particularly important challenge for asymmetrical networks that require multidirectionality, with links from one TRX to multiple distributed TRXs. Additional beam steering elements and laser sources are required to achieve such multidirectional communication when using conventional point-to-point active links. This escalates the system's power, mass, costs, and complexity for large numbers of links. To address this issue, this work introduces a passive architecture to achieve the goal of multidirectional communication for asymmetrical networks and the goal of high data rates for all-optical networks. The goal to establish multidirectional communication, without increasing the power and number of beam steering elements, can be met by implementing a passive uplink via retromodulation. Retro-modulation harnesses the optical power from an active downlink (DL). The DL beam undergoes modulation and retroreflection at the passive TRX to form a passive uplink (UL). Such passive ULs enable multidirectional communication, while eliminating pointing-acquisition-tracking, and support communication with an arbitrary number of TRXs within the retroreflector's field-of-view (FOV) [5]. Given such operation, the passive UL witnesses its greatest benefits for deployments communicating with many distributed active TRXs. The first benefit of the passive UL is that its use of retroreflection makes the system relatively insensitive to misalignment. This can minimize pointing loss that results from vibrations and platform jitter on aerial TRXs, which is a major challenge [2]. The second benefit of the passive UL is that its use of retroflection reduces the passive TRX's power requirements. The vast majority of the power is instead applied by the active TRXs, where the design constraints for mass and power are often less stringent. However, passive ULs are not commonly implemented due to the limited speed of contemporary free-space mechanical [6] and liquid crystal [7] modulators, operating at kilobit-per-second data rates. In response, recent studies have investigated passive ULs with electro-optical implementations, such as multiple-quantum-well modulators combined with corner cube [8,9] and multi-element (cat's eye) retroreflectors [5,10]. Data rates up to 45 megabit-per-second have been demonstrated, with the potential for gigabit-per-second speeds [11]. With the above technologies in mind, this work introduces an all-optical implementation of passive ULs, which carefully integrates an all-optical modulator [12] and a spherical (cat's eye) retroreflector [13] to realize a wider FOV and higher all-optical data rates.
The goal to achieve high (ideally terabit-per-second) data rates can be met by overcoming the fundamental bandwidth bottleneck between optics and electronics, which results from the use of far slower (gigabit-per-second) electronic processing and modulation [3]. This can be achieved by employing all-optical modulation, as opposed to electro-optic modulation, at the passive TRX [14]. In this work, all-optical modulation is implemented through cross absorption modulation, whereby a control (pump) beam linearly modulates the absorption seen by a coincident signal (probe) beam. The proposed cross absorption modulation scheme uses a control beam with a wavelength on resonance with the semiconductor's bandgap to generate free-carriers in the conduction band. These free-carriers induce a change to the semiconductor's refractive index, Δn, and absorption, Δα, by way of free-carrier absorption and/or state-filling [14]. This approach improves the nonlinear response and avoids the need for phase-matched propagation over centimeter lengths [15]. However, this approach leads to an additional constraint, whereby the generated free-carriers must recombine sufficiently fast to enable high data rates. This issue is solved by using a low-cost thin film of cupric oxide (CuO) nanocrystals, for which the generated free-carriers undergo ultrafast relaxation and recombination [14,16]. Ultimately, this nanocrystalline material is implemented with a spherical retroreflector to realize an effective all-optical retro-modulation (AORM) architecture for passive ULs. As a proof of concept, a link budget analysis of passive ULs is presented as well as theoretical and experimental studies of the proposed AORM architecture.

Methods
The passive UL formed by the AORM architecture must enable multidirectionality with minimal power, as stated for this work's main motivation. To quantify the effectiveness of AORM, link budgets can be used to compare passive ULs to contemporary active ULs.
The most common form of active UL uses a collimated line-of-sight beam directed between two TRXs. The detected signal power, Pdet, for this active UL is described by the Friis transmission equation [17] where η is the link loss (which is predominantly due to turbulence for links greater than 1 km) [18], P t is the transmitted beam power, A r as the receiver's area, Ω t is the solid angle defined by the beam's divergence, and R is the link length. Reflection losses are ignored in Eq. (1), as antireflective coatings can be implemented. The beam's solid angle is defined by the laser source, and can be described by the traditional antenna equation, being the square of the wavelength divided by the area of the source's aperture [17]. A wavelength, λ, of 1550 nm is chosen to meet eye safe constraints, enable compatibility with fibre optic telecommunication systems in the C band, i.e., 1530-1565 nm, and fall within the atmospheric transmission window from 700 nm to 1600 nm [2]. At this wavelength, Ωt will be limited by the aperture size of the source. For example, a 10-cm-diameter optical beam with a wavelength of 1550 nm will have a divergence-limited solid angle on the order of Ω t ≈3 × 10 −10 steradians (sr), which has been achieved in some recent FSO systems [19,20]. For an active UL with this narrow solid angle, and thus narrow FOV, multiple links to distributed TRXs can only be established by using several independent lasers and beam steering elements. This can be impractical for large numbers of links. An alternative approach to implement an active UL makes use of broadcasting over a wide solid angle. Broadcasted active ULs avoid the need for multiple independent beamsand are typical for radio-frequency links. However, the inverse-square power loss according to Eq. (1) becomes very large for long links broadcasting over a wide solid angle, which makes broadcasting impractical for FSO communication systems.
To resolve the conflicting demands for the above collimated and broadcasted active ULs, a passive UL can be used. An isolated passive UL is illustrated in Fig. 1(a), and multidirectional operation is illustrated in the inset. For each link, a collimated beam (shown in orange) is directed from the i th active TRX to the passive TRX, where a fraction of the beam area (shown in green) is modulated and retroreflected back to the active TRX. The resulting detected signal power at the active TRX for the retroreflected passive UL is where P t is the transmitted beam power, M is the all-optical modulation depth, A s is the retromodulated area of the signal beam, and Ω r is the retroreflected divergence solid angle. Reflection losses are ignored in Eq. (2), as the appropriate reflective and antireflective coatings can be implemented. Note the retro-modulated area, A s , and the receiver area, A r , are assumed to be smaller than the incident beams' areas. Also the total link losses, η, as a result of beam spread from atmospheric turbulence, can be a concern for long-range links with the active TRX at low elevations where turbulence is relatively close to the source. For example, the mean losses can range from 3 dB for long-range ground-to-satellite links to 0.03 dB for high altitude platforms [19,21]. For this work, near-and mid-range distances are considered, where these losses can be ignored. Based on Eq. (2), the passive UL is feasible as long as the power penalties associated with a small modulated signal beam area, As < Ω t R 2 , a large retroreflected divergence solid angle, Ω r > A r /R 2 , and a small modulation depth, M < 1, do not decrease the detected signal below the receiver's sensitivity. These three link budget conditions are considered in the design of the AORM architecture. The active DL has a continuous-wave beam (orange) with a solid angle of Ω t transmitted from the i th active TRX to the passive TRX. The passive UL has a portion of the incident beam be retro-modulated over an area of A s to create the retro-modulated signal beam (green) with a solid angle Ω r . This beam is retroreflected back to the active TRX, which has a receiver area of A r . The inset depicts multidirectional communication with an arbitrary number of active TRXs. (b) The proposed AORM architecture uses a glass sphere to collect the beam (orange) and focus it through a thin film of CuO nanocrystals, after which it retroreflects back to the active TRX. The on-board control beam (red) is focused with external optics onto the CuO thin film, with an area of A c , to modulate the signal beam (green) with a cross-sectional area of A s .
The design of the AORM architecture, depicted in Fig. 1(b), is based upon a spherical retroreflector, realized as two glass hemispheres that form a full sphere. The glass has a sufficiently high refractive index to have incident light rays focus onto the back surface [22], leading to retroreflection over a full 2π-steradians FOV. The incoming continuous-wave beam (shown in orange) is collected by the sphere. The outgoing signal beam (shown in green) is retro-modulated over a cross-sectional area of A s . Between the two hemispheres there exists a thin film of CuO semiconductor nanocrystals. The incident beam is focused through the CuO thin film and onto the sphere's back interface, where it is reflected and directed back to the active TRX (where the active TRX acts as the UL receiver and DL transmitter). At the same time, the control beam enters from the sphere's back interface and is focused with external optics onto the CuO thin film over an area of A c . The CuO thin film enables highly nonlinear interactions between the signal and control beams via cross absorption modulation on an ultrafast timescale with a modulation depth of M. Ultimately, the modulated signal beam is retroreflected back to the active TRX, forming the passive UL seen in Fig. 1(a). Note that the FOV for the AORM architecture will not cover the full 2π sr of the hemisphere, being the solid angle for effective retroflection, as modulation must also be considered. Specifically, less signal beam power will pass through the modulated area A c for large incident angles with respect to surface normal (i.e., z axis). If the FOV is defined by the solid angle over which the modulated signal power is equal to or greater than one half the modulated signal power at normal incidence, the FOV for effective retro-modulation is π sr.
The envisioned passive UL, with the proposed AORM architecture, can be implemented with a variety of formats for modulation and detection. However, amplitude-shift keying modulation with phase-locked self-homodyne coherent detection is particularly appropriate format. Such modulation and detection has a proven track record in passive optical networks [23][24][25]. Moreover, coherent homodyne detection offers unrivalled sensitivity, due to its inherent spatial and wavelength selectivity, and this has even supported its use in long-range terrestrial links [26] and intersatellite links [27]. It is also worth noting that the proposed passive UL is well suited to phase-locked self-homodyne detection because the laser on the active TRX can be used for both the signal beam and the phase-locked local-oscillator beam [28]. With such phase-locked self-homodyne detection, the phase-locked local oscillator beam can be used to introduce deconstructive interference on the carrier. Thus, any residual unmodulated carrier can be suppressed, if the modulation depth is small, M << 1, thereby eliminating the DC background power and its associated shot noise during detection [28,29]. Detection can also be implemented with balanced detectors to lessen relative intensity noise (RIN) and amplifier noise [29,30]. For all these reasons, phase-locked self-homodyne detection is well suited to passive ULs.

Theoretical results
The three link budget conditions stated in the prior section are considered here for the proposed AORM architecture.
The first condition defined by the link budget for AORM requires maximizing the modulated signal beam area, As, which can be accomplished by careful placement of the CuO thin film within the spherical retroreflector. Increasing A s will, however, also increase the control beam's modulation area, A c , as shown in Fig. 1(a). It is desirable to reduce A c for the same control beam power, P c , as the intensity, P c /A c , is linearly proportional to the modulation depth, M. This conflicting relationship between A c and A s can be minimized by placing the CuO thin film at the sphere's centre, in the z = 0 plane, as seen in Fig. 1(b). At this location, the control beam, with an area of A c = πa 2 /4, modulates a signal beam area of A s = πa 2 , where a is the radius of the sphere. For comparison, the CuO thin film could cover the entire back curved surface of the sphere. However, for this case, the control beam would need to have a larger area, of A c = 2πa 2 , to modulate the same signal beam area of A s = πa 2 . Ultimately, the z = 0 plane offers a factor of eight improvement to M, for the same P c , over that of the back curved surface. Furthermore, the FOV, for which the signal beam can be retro-modulated, must be considered. For the case with a CuO thin film in the z = 0 plane, the FOV will remain constant regardless of the control beam area, A c . (In contrast, for the case with a CuO thin film on the back curved surface, the FOV will decrease for a smaller A c . This same challenge would apply to the aforementioned multi-element (cat's eye) retroreflector, where the signal beam is focused onto the modulator at a location off of the optical axis [5,10].) This independence between the FOV and control beam area, A c , for the CuO thin film in the z = 0 plane is an important attribute because it allows the control beam area to be varied without penalty. It will be shown later in this work that decreasing A c enhances the retroreflected divergence angle.
The second condition defined by the link budget for AORM requires minimizing the retroreflected divergence solid angle, Ω r . The goal is to achieve the same level of collimation for the retroreflected beam as the transmitted beam. The required level of collimation is dependent upon the application's given link distance, R. The smallest achievable beam radius, ω 0 , at a distance R is limited by the Rayleigh range, z R , being z R = πω 0 2 /λ. For the near-and mid-field beams, where R < 10z R , it can be shown using standard Gaussian beam analysis that the smallest beam radius will be ω 0 = (λR/π) 1/2 , assuming that a beam expander is used at the active TRX [31,32]. Otherwise, the beam radius at a distance R will be limited by the aperture size of the TRX's telescope. Thus, the required divergence solid angle for the near-and midfield range is Ω r < λ 2 /(πω 0 2 ) = λ/R. At a wavelength of λ = 1550 nm, links with distances of 100 m, 1 km, and 10 km, would require Ω r to be on the order of 10 −8 sr, 10 −9 sr, and 10 −10 sr, respectively. For the purposes of this work, the nominal case with a distance of 1 km and divergence solid angle of 10 −9 sr will be studied to assess the link's feasibility.
The main source of divergence that could increase Ω r beyond the 10 −9 sr diffraction limit is spherical aberration introduced by the spherical retroreflector. Spherical aberration manifests itself as an increasing divergence angle for retroreflected rays that are increasingly far from the optical axis (OA). There are two solutions to mitigate it: decrease the control beam area, A c , or design the spherical retroreflector to compensate for spherical aberration.
The first solution to mitigate spherical aberration is to decrease the control beam area, A c , with respect to the sphere's size (or, equivalently, increase the sphere's size with respect to A c ). Decreasing A c will decrease the area of the incoming beam being modulated, as seen in Fig. 1(b). These rays, being sufficiently close to the OA, will undergo less spherical aberration and thus exhibit a low divergence solid angle, Ω r , on the retro-modulated beam. The resulting Ω r is depicted in Fig. 2 as a function of the control beam radius, r c , normalized to the sphere's radius, a, for various spherical retroreflectors. The results of Fig. 2 are calculated via a MATLAB ray tracing simulation, based on the laws of reflection and refraction, which was developed to analyze the spherical geometries of interest. Beginning with an ideal spherical retroreflector, implemented as a glass sphere with a refractive index of n = 2.000 (black), it is seen that a smaller r c achieves a low Ω r . Specifically, a low beam divergence of Ω r < 10 −9 sr can be achieved with r c being approximately 2% of a. However, it would be difficult or impossible to find a material with a refractive index of exactly n = 2.000 for use in the telecommunication C band. The closest material is S-LAH79 glass with a refractive index of n = 1.955 at a wavelength of 1550 nm. The resulting Ω r for the S-LAH79 retroreflecting sphere is displayed in Fig. 2 (shown in red). Sufficient beam divergence for a 1 km link can be achieved with r c being approximately 0.02% of a. However, this retroreflector would be impractical for a 10 km link as r c would need to be approximately 0.006% of a to achieve the needed Ω r < 10 −10 sr. It is important to note that the impracticality of reducing r c , or alternatively increasing a, does not come from performance constraints. It comes instead from practical constraints, such as the diffraction-limited spot size of the control beam, maximum practical sphere size, laser-induced damage, free-carrier saturation, and thermal fluctuations. The details of such constraints are discussed in the upcoming section. However, reducing r c , and thus A c , is one of the major advantages of the proposed architecture, as it will not affect the retroreflector's FOV or overall detected signal power, P det . This is because the CuO thin film is at the sphere's centre. This claim is based on Eq. (2), where one might expect P det to decrease for a decreasing A c , because there will be a corresponding decrease in the signal beam area, A s . However, the modulation depth, M, in the equation is proportional to the control beam intensity, P c /A c , so P det will also increase in proportion to 1/A c . Thus, assuming no practical constraints, there is no performance penalty for reducing A c . Fig. 2. Ray tracing simulations of the retro-modulated divergence solid angle, Ω r , as a function of the control beam radius, r c , normalized to the sphere's radius, a, for various spherical retroreflectors. The following non-cladded and cladded spheres are presented: an ideal n = 2.000 sphere (black), an n = 1.955 sphere (red), an n = 1.955 sphere with an n = 1.500 cladding (blue dash), and an n = 2.500 sphere with an n = 2.301 cladding (green). The goal of Ω r < 10 −9 sr is achieved for portions of the curves below the displayed horizontal dashed line.
The second solution to mitigate spherical aberration is to use a spherical retroreflector with a gradient refractive index [33] or a concentric cladding [34]. Such retroreflectors have been tested in space [35]. The concentric cladding retroreflector is of particular interest here, due to its lesser manufacturing complexity and improved performance through careful material selection [34]. A sphere with a single concentric cladding, with both materials having refractive indices below n < 2, can be used to attain the same divergence as an ideal n = 2 sphere. Based on two chosen refractive indices, being for the outer cladding, n 1 , and inner sphere, n 2 , the corresponding ratio of radii can be determined from lens theory to be r 2 /r 1 = (1/n 2 -1/n 1 ) / (1/2 -1/n 1 ) [34], where r 1 = a. It is preferable for the interior material to have a refractive index close to n = 2.000, such as S-LAH79 glass with n 2 = 1.955, and the cladding material to be a typical polymer or glass with a refractive index near n 1 = 1.5. The resulting Ω r for these two materials, with n < 2 and r 2 /r 1 = 0.931 ± 6 × 10 −4 , shown in Fig. 2 (blue dash), matches that of the ideal n = 2.000 sphere. The tolerance is defined such that half the signal power achieves the desired Ω r < 10 −9 sr for the same control beam radius. Such a structure, combined with a small A c , is a simple way to reduce spherical aberration with minimal manufacturing complexity. This structure can be further improved to nearly eliminate spherical aberration by using materials with refractive indices above n > 2. For this case, the refractive index of the interior material depends upon the refractive index of the exterior cladding material and vice versa. For a hypothetical pair of materials, with n 1 = 2.500 and n 2 = 2.301 ± 2 × 10 −3 and r 2 /r 1 = 0.34594 ± 1 × 10 −4 , the resulting Ω r is displayed in Fig. 2  (shown in green). For this structure, a beam divergence of Ω r < 10 −9 sr can be achieved with r c being approximately 7% of a. However, to the authors' knowledge, materials with these sufficiently high and precise refractive indices do not exist. A structure with a second cladding layer can be implemented to alleviate this constraint, as demonstrated by Oakley [34]. The main benefit for a sphere with two claddings is that it can facilitate a smaller sphere, with a four times smaller radius, to achieve the same retroreflection capabilities (i.e., the same divergence with the same r c ) as the single cladding structure with n < 2. However, this reduction in size comes at the expense of greater manufacturing complexity, so the choice between single cladding and dual cladding structures will depend upon the level of performance that is needed in the application.
Two additional sources of divergence are also considered here, being the size of the spherical retroreflector and the size of the modulation area.
The sphere's size can introduce divergence beyond the diffraction limit if the sphere's radius, a, is smaller than the incident beam's radius. For a 1 km link, the minimum incident beam radius, ω 0 , would be approximately 2.2 cm, and thus a > ω 0 should be chosen. For example, a valid implementation could use a 5-cm diameter sphere with an applied control beam of r c = 0.5 mm (for the n 1 = 1.955, n 2 = 1.50 cladding) or r c = 1.7 mm (for the n 1 = 2.301, n 2 = 2.50 cladding). Either implementation yields low spherical aberration and acceptable divergence.
Increased divergence can also occur from the induced modulation over the control beam. Assuming that amplitude shift keying is used, the control beam will be on for only one of the two binary symbols. Thus, when the control beam is off, the signal beam will undergo the standard diffraction-limited divergence that is defined by the spherical retroreflector. However, when the control beam is on, the signal beam will undergo increased diffraction. This response is in fact advantageous because the control beam being on both decreases the signal beam power and increases its divergence (because it is missing the central area of its beam profile). Thus, the modulation depth of the received signal beam will be improved beyond that expected solely from the decreased signal power. Future investigations could tailor the profile of the modulated area to optimize the far-field pattern of the signal beam for enhanced modulation.
The third condition defined by the link budget for AORM requires increasing the alloptical modulation depth, M. In this work, M is defined as the percent change in signal beam power, M = |ΔPs/Ps|. In general, M is linearly proportional to the material's change in refractive index, Δn, and change in absorption, Δα, induced by the control beam. Fibre and waveguide structures typically employ a Δn material response via nonresonant nonlinearity, which requires phase-matched propagation over centimeter lengths due to a low third-order nonlinear coefficient [15]. In our previous work, for short-range optical wireless communication, we used nonlinear glass to retro-modulate the signal beam [36]. The refractive index of a glass-air interface was modulated according to M = 4Δn/(n 2 -1) with negligible Δα. The findings suggested that a stronger nonlinearity is required-and this work does so, in the manner shown in the following section. A 10 3 improvement in M is measured.

Experimental results
The proposed AORM architecture is experimentally tested to find the modulation depth and the maximum data rate. Cross absorption modulation is implemented via the proposed CuO thin film because it has a strong change in absorption, Δα. This leads to a large modulation depth, M = δΔα, where δ = 200 nm is the measured 1/e penetration depth for CuO. For films thinner than the 1/e penetration depth, δ is equal to the film thickness. Note that modulation due to the control-beam-induced change in refractive index, Δn, was measured and found to be negligible, at approximately 2% of the modulated power due to Δα. Ultimately, CuO is selected because the control beam is on-resonance with its bandgap and the resulting photogenerated free-carriers produce a strong Δα material response via free-carrier absorption and state-filling effects. More details on the ultrafast dynamics of CuO are given in our earlier study [16].
Experimental tests are carried out for a 20 nm thick CuO thin film with nanocrystal diameters of 50 ± 20 nm. To create the CuO phase, a 20 nm film of sputtered copper is annealed at 600°C for one hour in ambient air [16]. This thickness was chosen as it provides the best structural uniformity, spectral absorption characteristics, and signal-to-noise ratio. The CuO thin film is deposited on the flat face of an S-LAH79 glass hemisphere, which is then coupled to another S-LAH79 hemisphere to form a full sphere. The S-LAH79 glass is chosen here as a proof of concept architecture for retro-modulation. The aforementioned complex retroreflectors can also be fabricated with this process if there is a need for longer distance links.
The AORM architecture is characterized by measuring the ultrafast impulse response to determine M and the maximum achievable data rate. The 775-1550 nm time-resolved pumpprobe experimental setup is used to measure the ultrafast characteristics and is depicted in Fig. 3(a). This time-resolved technique enables measurements of ultrafast events with slow electronic equipment, whereby the resolution is limited only by the pulse duration. The signal (probe) beam with a wavelength of 1550 nm is used. This relatively long wavelength for the signal beam makes it more sensitive to free-carrier absorption because such absorption has a squared dependence on the wavelength. The control (pump) beam is generated at a wavelength of 775 nm by second-harmonic conversion of the signal beam. The laser source for both beams is an erbium-doped fibre laser with a measured pulse duration of 150 fs and repetition rate of 90 MHz. The 1550 nm signal beam (orange) is introduced via a 50-50 beamsplitter and compressed with a telescope before incidence on the AORM architecture, as depicted in Fig. 3(a). (Note that for a real-time communication system, the signal beam would be a continuous-wave source.) The AORM architecture is tilted at five degrees to ensure that reflections not due to retroreflection are eliminated. The antiparallel 775 nm control beam (red) is focused with a 20 × microscope objective onto the CuO thin film. The retromodulated signal beam is measured using an InGaAs detector and a lock-in amplifier (Stanford Research Systems, SR830) with a 300 ms time constant. With such a setup, the system is able to carry out time-resolved data acquisition to capture the femtosecond optical response. The measured modulation depth is presented in Fig. 3(b) as a function of the time delay between the control and signal pulses. A modulation depth of M = 2 × 10 −4 is measured for an incident control beam fluence of 5 μJ/cm 2 , with a beam radius of r c = 15 μm. Approximately 10% of the incident control beam power is absorbed by the 20 nm thick film, resulting in an absorbed fluence of 0.5 μJ/cm 2 . This fluence was chosen due to thermal effects that were observed for absorbed control beam fluences above 1 μJ/cm 2 , due to a slight heat-induced expansion of the mated glass hemispheres. Such expansion manifests itself as a slow transient drift in the measured signal power (over many seconds) following the introduction of the control beam. This impacts the pump-probe experimental measurements, as the signal is acquired with a time-resolved measurement technique, as a function of the pump-probe delay, over many minutes. However, for steady-state (real-time) operation, this transient drift would not be a concern, as it could be eliminated by a simple high-pass electronic filter. Furthermore, the CuO thin film was tested on an isolated glass substrate. No limitations due to thermal effects, laser induced damage, or free-carrier saturation were observed up to the maximum control beam fluence achieved by our experimental setup, using a 20 × microscope objective and an average control beam power 44 mW, resulting in 26 µJ/cm 2 absorbed by the CuO thin film. At this fluence, a maximum modulation depth of M = 1 × 10 −2 can be realized, and it is likely that larger modulation depths can be achieved with higher control beam fluences. If thermal effects, laser induced damage, or free-carrier saturation become an issue at higher repetition (i.e., data) rates than the 90 MHz experimentally tested here, r c can be increased to decrease the control beam fluence. This would not decrease the received signal power because the decrease in modulation depth due to the decreased control beam fluence would be compensated for by a proportional increase in the modulated area of the signal beam.
The experimental impulse response, presented in Fig. 3(b), characterizes the maximum speed of the AORM architecture. The retro-modulated signal beam is shown to have an effective recovery time constant of 770 fs. This experimental result indicates that the AORM architecture could support high aggregate data rates, with multiple channels, whereby the data rate per channel is limited by the detected power and relevant noise sources. The multiple channels could be established via all-optical time-division multiplexing and demultiplexing at each TRX-in an analogous manner to that applied in fibre optic links [37,38].

Discussion
To quantify the performance of the AORM architecture in this work, the experimentally measured result of the modulation depth for a given the control beam fluence can be substituted into Eq. (2). The modulation depth can be reformulated as M = δΔα = δβEc/Ac, where β is the modulation constant for cross absorption modulation and E c is the energy of a bit/pulse in the control beam. The control beam power is related to E c by P c = E c B, where B is the bit rate. Based on the measured modulation depth, CuO film thickness of 20 nm, and control beam fluence, the modulation constant is β = 200 cm/μJ. The link is assumed to use the aforementioned phase-locked self-homodyne coherent detection method to remove the shot noise associated with the large carrier background power. The resulting detected signal power at the active TRX would be P det = 4δβP c P t A r / (BΩ t Ω r R 4 ), where the signal beam area is approximately A s ≈4A c , as a result of the sphere's 2 × magnification. The divergence solid angle of the transmitted beam, Ω t , is set to a limit of 10 −9 sr. The retro-modulated retroreflected beam, Ω r , can also be set to 10 −9 sr, assuming a sufficiently large sphere, such as a 5-cm diameter sphere, and a control beam radius, r c , that is sufficiently small with respect to a, as defined by the region below the horizontal dashed line in Fig. 2. With such low divergence over a distance of 1 km, it is assumed that the entire retro-modulated signal power can be collected with a practically sized TRX receiver area, giving A r /(Ω r R 2 ) ≈1. The implemented AORM architecture is assumed here to use a CuO thin film with a thickness that is greater than or equal to the penetration depth, being δ = 200 nm, to have it fully absorb the control beam energy. For a single channel bit rate of 1 gigabit-per-second, a transmitted power of P t = 1 W, and an average control beam power of P c = 1 W, the detected power is calculated to be P det = 4δβP c P t / (BΩ t R 2 ) ≈1.6 μW. If shot-noise-limited performance is assumed, the signal-to-noise ratio (SNR) is (RP det ) 2 / (2eRP det Δf) = 37 dB, where R = 1 is the responsivity, e is the elementary charge of an electron, and Δf is the bandwidth, which is approximated here by the bit rate B. This is a strong SNR, but it would be reduced if the single channel bit rate is increased or other noise sources are introduced, such as relative intensity noise (RIN) and shot noise due to residual power from the carrier. For this link budget, the maximum achievable single-channel bit rate would be approximately 20 gigabitsper-second with an SNR of 10 dB. Multiple links with additional TRXs could be established at the single channel data rate via all-optical time-division multiplexing, with the aggregate data rate ultimately limited by the material response time of 770 fs, giving an upper limit for the bandwidth of 1.3 THz.

Conclusion
In conclusion, the presented work put forward new technologies for FSO and OWC asymmetrical all-optical networks. The proposed system applied direct laser transmission for the active DL and a new AORM architecture for the passive UL. It was shown that such a system can function with multiple active TRXs, over wide service coverage, and one passive TRX, that requires low power and mass. Such an asymmetrical system would be well suited for communication with unmanned aerial vehicles [39] and high-altitude platforms [19,40]. The AORM architecture used high-refractive-index hemispheres to realize effective retroreflection, and an interior CuO thin film to realize ultrafast all-optical modulation between co-incident control and signal beams. The AORM architecture was fabricated and tested. It was found to have an ultrafast recovery time of 770 fs with a modulation depth of 2 × 10 −4 for an absorbed control beam fluence of 0.5 μJ/cm 2 . The maximum modulation depth was measured to be 1 × 10 −2 corresponding to the highest (experimentally achievable) absorbed control beam fluence, being 26 μJ/cm 2 . As future work, the modulation depths and overall performance can be improved. Specifically, the modulation could be increased through the use of resonant structures, such as a Mie resonator [41,42] or Salisbury screen [43]. Such resonators have the transmission of the signal beam become increasingly sensitive to control-beam-induced material perturbations. Further improvements could include adding a standard (thin film) antireflective coating to the spherical retroreflector's front surface. As only the paraxial rays are modulated by the AORM architecture, there would be no concern for varying incident angles with such a coating. A metallic coating could be added to the spherical retroreflector's back surface to enhance its reflection, although it would require a small opening for entry of the control beam. For this opening, a dichroic filter could be used to reflect the 1550 nm signal beam and pass the 775 nm control beam. Ultimately, the findings from the presented work can lay the foundation for future implementations of multidirectional FSO and OWC systems with terabit-per-second data rates.

Funding
Natural Sciences and Engineering Research Council of Canada (341487-12); Canadian Foundation for Innovation (LOF 16659); Western Economic Diversification.