Application of Holograms in WDM Components for Optical Fiber Systems

Coarse Wavelength Division Multiplexing (CWDM) technologies are being widely deployed internationally in metropolitan and access networks due to the increased demand for delivering more bandwidth to the subscriber, created by the need of enhanced services, (Koonen, 2006). For metro, and mainly for access networks applications, an increment in capacity may be achieved with a cost-effective multiplexing technology without the need for the high channel counts and closely spaced wavelengths typically used in long haul networks. A channel space of 20 nm, as proposed in the G. 694.2 ITU Rec., can be used relaxing the processing tolerances and potentially lowering the cost of components. CWDM technology reaches those requirements and it has been proposed for these applications. It is in this context that holographic optical devices have a potential use. This chapter describes the theory, design, and experimental results of a generic multipurpose device that can operate as a tunable wavelength filter, wavelength multiplexer and wavelength router. This device could be especially useful in optical network applications based on both Coarse and Dense Wavelength Division Multiplexing technology (CWDM/DWDM). The enabling component is a Ferro-electric Liquid Crystal (FLC) Spatial Light Modulator (SLM) in which dynamic holograms are implemented in real time. As a consequence, the device will be able to carry out different functions according to the hologram recorded on the SLM. The great advantage of this device is polarization insensitivity in the region of operation, allowing low cross-talk and simple handling. As hologram management is the basis for this device, some topics in the Computer Generated Hologram (CGH) design process are commented on and general guidelines are also considered. Laboratory experiments have demonstrated the capability of a phase FLC-SLM, with the great advantage of polarization insensitivity operation, to diffract the incident light according its wavelength and hologram patterns, for the use in the former applications. Two typical applications of this technology are described: the first one is a design of an equalized holographic Reconfigurable Optical Add-Drop Multiplexer ( ROADM), where this device can address several wavelengths at the input to different output fibers, according to the holograms stored in a SLM (Spatial Light Modulator), all the outputs being equalized in power; the second one is dealing with the design of an holographic router with loss compensation and wavelength conversion whose main application is in Metro networks in the interconnection nodes. This device uses a SOA (Semiconductor Optical Amplifier), in the non linear region, to do the wavelength conversion and, in addition, to supply the gain in order to compensate for the intrinsic losses of the holographic device.


Introduction
Coarse Wavelength Division Multiplexing (CWDM) technologies are being widely deployed internationally in metropolitan and access networks due to the increased demand for delivering more bandwidth to the subscriber, created by the need of enhanced services, (Koonen, 2006).For metro, and mainly for access networks applications, an increment in capacity may be achieved with a cost-effective multiplexing technology without the need for the high channel counts and closely spaced wavelengths typically used in long haul networks.A channel space of 20 nm, as proposed in the G. 694.2 ITU Rec., can be used relaxing the processing tolerances and potentially lowering the cost of components.CWDM technology reaches those requirements and it has been proposed for these applications.It is in this context that holographic optical devices have a potential use.This chapter describes the theory, design, and experimental results of a generic multipurpose device that can operate as a tunable wavelength filter, wavelength multiplexer and wavelength router.This device could be especially useful in optical network applications based on both Coarse and Dense Wavelength Division Multiplexing technology (CWDM/DWDM).The enabling component is a Ferro-electric Liquid Crystal (FLC) Spatial Light Modulator (SLM) in which dynamic holograms are implemented in real time.As a consequence, the device will be able to carry out different functions according to the hologram recorded on the SLM.The great advantage of this device is polarization insensitivity in the region of operation, allowing low cross-talk and simple handling.As hologram management is the basis for this device, some topics in the Computer Generated Hologram (CGH) design process are commented on and general guidelines are also considered.Laboratory experiments have demonstrated the capability of a phase FLC-SLM, with the great advantage of polarization insensitivity operation, to diffract the incident light according its wavelength and hologram patterns, for the use in the former applications.Two typical applications of this technology are described: the first one is a design of an equalized holographic Reconfigurable Optical Add-Drop Multiplexer ( ROADM), where this device can address several wavelengths at the input to different output fibers, according to the holograms stored in a SLM (Spatial Light Modulator), all the outputs being equalized in power; the second one is dealing with the design of an holographic router with loss compensation and wavelength conversion whose main application is in Metro networks in the interconnection nodes.This device uses a SOA (Semiconductor Optical Amplifier), in the non linear region, to do the wavelength conversion and, in addition, to supply the gain in order to compensate for the intrinsic losses of the holographic device.

Operating principle
The working principle of a holographic device design is based on the wavelength dispersion produced in a diffraction grating element (Agrawal, 2002).When a polychromatic light reaches a diffraction grating, there is an angular dispersion (diffraction) according to the incident light wavelength.Equation (1) expresses the relationship between the diffraction angle and the wavelength of the incident light : (1) by considering the incident light perpendicular to the grating, Ф is the diffracted light angle, m is the diffraction order and d the grating spatial period.
The light diffracted, in a far field approximation, follows the Fourier transform distribution and the intensity for the different diffraction orders, m, is proportional to sinc 2 (Фd/ ); the separation between diffraction orders is given by R/d, where R is the distance between the binary transmissive diffraction grating and the Fourier plane (Kashnow, 1973).
Most diffraction grating elements are not practically useful for changing the spatial period or the wavelength.A way to allow these variations is, by using a Spatial Light Modulator (SML), to implement on it a Computer Generated Hologram (CGH).The pixelated structure of the SLM produces the effect of a two-dimensional diffraction grating when the device is illuminated with a coherent light.In the SLM every ferro-electric liquid crystal (FLC) pixel can be electro-optically configured to provide a phase modulation to the incident light.Therefore, by managing the hologram on the SLM and its spatial period a programmable diffraction grating is obtained.
In optical fiber communications, wavelengths around 0.8 -1.6 µm are used.Thus, an SLM pixel pitch close to these wavelength values is required.Unfortunately, current commercial SLMs do not have enough resolution.Therefore, to solve this limitation, a fixed diffraction grating with a low spatial period, together with the SLM giving a high resolution filter, is used (Parker et al., 1998

2 and 4-phases holograms
Different types of holograms can be used (Horche & Alarcón, 2004) in the SLM.In order to optimize losses, phase holograms are preferred instead of amplitude holograms due to its intrinsic 3 dB of loss and 4-phase holograms are used instead of 2-phase (binary) holograms because of its greater efficiency (40.5%  81%), which is proportional to sinc 2 (π/M), where M is the number of phases.Table 1 summarizes the relationships between phase and contrast for 2 and 4 phase holograms.

Computer generated hologram design
Taking into account the former considerations and by implementing a hologram on the SLM where its spatial period can be modified in real time, we obtain a programmable diffraction grating.
The relationship between the hologram and its Fourier Transform function are: In order to implement the CGH, holograms are calculated by using a program based on a variation of the widely adopted simulated annealing optimization algorithm (Dames, Dowling et al., 1991), (Broomfield, Neil et al., 1992) whose cost function to minimize the calculation error is: where I i 2 is the calculated spot intensity for the diffraction order i; A i 2 is its defined intensity and A 2 is the average intensity for the diffraction target spots; t is the number of process calculations.
There are three steps in a CGH design process: 1. Target definition: the target is the diffraction pattern that is to be obtained from the SLM.Depending on the use: filter, switch or others, this target is usually an array or a matrix of spots.This is the input for the program.2. Fourier transform calculation: the program calculates the inverse Fourier transform (F.T.) -1 of the target.The optimization algorithm compares the FT of the hologram with the defined target improving the efficiency at each calculation time.Hologram pixels are flipped between the amplitude values 0,  (or phase 0, π) to reduce an error function, (2), specifying the difference between the desired target in the Fourier plane and the reconstruction obtained from the current state of the hologram, improving the efficiency at each calculation (Efficiency defined as: η = Σ m orders diffracted light /total incident light).3. Finally, CGH implementation in an optical substrate, using a photographic film or SLM.The CGH designed for this work is a black & white bars pattern implemented onto a Spatial Light Modulator, where there are only two possible states: "1" for white (total transparency or π phase shift) and "0" for black (total darkness or 0 phase shift).Fig. 3 shows the original diffraction target (a), an array of spots with different light intensities (non uniform, as in Fig. 3a), and three consecutive holograms (b, c, d), calculated by the program carrying out the inverse FT according to the algorithm efficiency.A 45% efficiency is an initial calculation value and close to 90% efficiency is practically the best result in the optimization process.During the calculation of the hologram, the program can find out different holograms which match the diffraction target.It is possible to change, dynamically, the initial conditions (original diffraction target and efficiency, optimization process parameters), to change the direction for the optimization process allowing the algorithm to escape from local minima and reach the correct hologram.Computer calculations are very sensitive to the geometrical distribution of the original diffraction target.A very slight misalignment on it (centre: x = 0, y = 0) can produce a hologram completely different from the correct one.This effect is shown in Fig. 4 when the original array of spots (Fig. 4a) is shifted by 30% of spot separation δ (Fig. 4b), along the vertical axis y; the calculated target (Fig. 4c) is an array of spots "duplicated" and "shifted" instead of a singular one.
To avoid small misalignments, along the x axis, of the output fibers array positions , with impact on the efficiency, we can optimize the hologram pattern, introducing an offset in the bar positions to correct them (Crossland et al., 2000) An offset of 5% of the hologram period would impact the efficiency up to a 40%.
For the operation of holographic devices after the generation of holograms, it is necessary to configure with them the SLM.To perform the switching operation a closed control between the holographic component (SLM) and the computer is needed to assign the correspondent hologram from a local database.This procedure is represented in Fig. 5, where a switching control acts over the PC-SLMs interface. H

Dynamic holographic device design
In order to design a holographic optical device a "4f" structure is chosen using a transmissive SLM and fixed grating.Fig. 6 illustrates the device used in the present work.
The previously calculated CGH (black and white bars) is loaded onto the SLM via a PCbased interface.The SLM-FLC and fixed grating are illuminated by light coming from a singlemode optical fiber collimated by means of a lens.A second lens produces the replicated array of spots explained above on the back focal plane of the lens.
In our experiments, we are interested only in the array of spots corresponding to the first order of diffraction.Therefore, the output optical fibers array is placed in the back focal plane of the lens at a certain angle in order to optimize the coupling.Because of the small size of the singlemode fiber radius, it acts as a spatial light filter.Output fibers F 1 ,..,F 10 , must be located at the Fourier lens plane in order to receive the maximum light intensity of the diffracted beams.The relationship between the system diffraction angles (Parker et al., 1998) is in agreement with the expression: where x is the distance of the output optical fiber from the optical axis, f is the focal length of the lens, d is the spatial period of the fixed grating and H is the hologram spatial period, which relationship with D, the size of the pixel, and N, the number of pixels in one dimension of the SLM is given in (4): where n is the integer number of black & white bar pairs and depends on the type of hologram (pattern).For small angles, equation ( 3) can be simplified as follows: 1 1 When the other holographic device parameters are fixed, only depends on n, as can be shown from (5).According to fixed or variable values for n or/and x, different applications for our device can be considered giving an idea of the device's versatility (see Table 2).
In the following sections, we design a generic multipurpose device based on the experimental scheme explained above that can operate as a tunable wavelength filter, wavelength multiplexer and wavelength router, by simply modifying in real time the CGH loaded on the SLM.The PC-based interface used to load the CGH on to the SLM also serves to calculate the different patterns needed.The electronic interface allows an automatic program to be developed for loading different patterns when they are needed.In all cases, the central wavelength channel, 0 , is obtained for n = N/4 in (5), and the operating wavelength range Δ f is given by: The -3dB passband width, BW, for each wavelength channel tuned, is limited by the output fiber characteristics and the wavelengths coupled inside the core diameter φ core .Taking this into account, and from (3), the following expression relates the bandwidth BW for every wavelength channel tuned in the filter and the focal distance f of the lens according the optical power coupled into the output optical fiber (Parker et al., 1998): In order to obtain minimum losses, the collimated light through the SLM has to illuminate the maximum quantity of pixels.As its intensity distribution has a Gaussian profile, it is sufficient that 1/e 2 beam bandwidth illuminates the SLM aperture.According to optical Gaussian laws, the following condition is reached: For commercial FLC-SLMs, available pixel size D is > 5 µm and the number of pixels, N, usually is from 250 to 1000.From expressions ( 5) and ( 7), it is possible to calculate the x value and max and min for the operating range of tuning.

Tunable holographic filter application
In order to design a tunable holographic filter with a -3dB passband width, BW, of 1 nm (125 GHz), for each wavelength channel tuned, we take d = 3.5 µm for the spatial period of the fixed grating.To use the same device for CWDM/DWDM, a SLM with a value of N = 720 and D = 7 µm for the spatial period, is chosen.The output singlemode fibers used in our device have a core diameter, φ core , of 9 µm.Then, from (7), f must be greater than 23.9 mm.As a practical value we assume f = 25 mm.

Wavelength response
For CWDM applications the holographic filter has a tuning range of Δ f =1591 -1311 = 280 nm with a -3dB passband of 1 nm.In Fig. 7 the transmission response is shown, according to (Parker et al., 1998).For wavelengths very close to the centre, the shape is Gaussian ( < 0 +/-1,5 nm); from these wavelengths the shape is like a Bessel function and the zero convergence is slower ( > 20 dB for > 0 +/-1,5 nm ; > 40 dB for > 0 +/-5 nm).
Table 5 shows, in case of CWDM systems, the different values of n and corresponding central wavelengths separated by 40 nm, from 1311 to 1591 nm.In this case, an adjacent channel isolation > 50 dB is achieved and the complete filter tuning range is covered according to the type of hologram.

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This feature allows the possibility of a multiple pass band filter in the same optical fiber, but with an increment of losses penalty according to the expression 10 log C (dB), where C is the number of simultaneously tuned channels (Parker et al., 1998).In this case, C = 4 and therefore the increment of losses in the device is: Δ losses = 10 log 4 = 6 dB.

Loss estimation
There are three different sources of loss in this holographic device: a. SLM losses An FLC-SLM works as a dynamic full π-binary phase fixed grating hologram with a diffraction efficiency η = 36.5% (4.38 dB) for the first diffractive order (m =1) and a FLC switching angle of 45º.
Another cause of losses is the insertion of the hologram, for a phase SLM, as a result of the light polarization plane and FLC switching angle different to 45º (theoretical optimal angle); at least another 2 dB are lost, assuming a good alignment of the collimated input light and the FLC pixels.b.Fixed grating losses The diffraction efficiency for a fixed grating, binary π-phase, is η = 36.5% for the first diffractive order (m=1).That means a loss of 4.38 dB.c.Fiber/lens coupling efficiency A fiber/lens coupling efficiency of 50% is a good approximation; therefore another 3 dB of losses have to be added (2 dB, with very good alignment).
Losses can be improved using multiple-phase or blazed gratings; in this case the efficiency can reach η ≈ 80 -90% and the losses decrease to 1.5 dB (Ahderom, Raisi et al., 2002).

WDM (wavelength division multiplexing) application
We can use this device as a 1x M demultiplexer, where M is the number of output fibers.For this, a fixed value of n is used and the output fibers are located in certain x positions.Output fibers (9/125 µm) must be placed in agreement with the diffracted angles Ф, according to input wavelengths and they have to be separated at least Δx = 125 µm.From (5), we can calculate the Δx taking the value of center to center wavelength channel separation, Δ , into account: In order to design a compatible device with the frequency grid provided in ITU-T G.694.1/G.694.2Rec. for CWDM/DWDM systems, a 1x4 demultiplexer (M = 4) for DWDM1 with Δx = 161 µm and a 1x8 demultiplexer (M = 8) for CWDM with Δx = 321 µm, can be implemented.
Table 6 summarizes the fiber positions in order to demultiplex the wavelengths used in the CWDM/DWDM systems.A CWDM system uses F 1 , F 2 , F 3 , F 4 , F 5 , F 6 , F 8 and F 10 and a DWDM uses F 7 , F 8 , F 9 , and F 10 output fibers (see Fig. 6).It is necessary to emphasize that a better performance as demultiplexer could be implemented if only this function is required.
For example, we could design a demultiplexer device with channel separation smaller than 50 GHz (Parker, Cohen et al., 1997).However, the novel idea is to design a compatible CWDM/DWDM device able to carry out different functions.

Wavelength routing application
Maintaining output fibers in the same place as shown in Table 6, if n value (type of hologram) is properly varied, a certain wavelength coming from the input fiber can be routed to any one of the output fibers.As an example, Table 7 highlights the n values for routing 0 = 1431nm (CWDM) and 0 = 1551 (DWDM) towards an output fiber; these values have been calculated from (10), considering the variation of n according to Δx: For Δx = 161 µm, Δn was calculated by using (10) resulting in Δn = 21 and for Δx = 321 µm, Δn is 45.Therefore, the device is a 1x8 router in case of CWDM and a 1x4 router for DWDM systems.It is necessary to highlight that the positions of the fibers are compatible with all applications and that the crosstalk resulting from high-order diffraction beams (m =  2,  3,.) are outside of the locations of the output array fibers (ΔФ = 4º), (Horche, 2004).

Basic experimental results
In this section two complementary experiments have been made.The first one is related to diffraction patterns measurements for different bars holograms and the second one to a SLM characterization for holographic filters, demultiplexers and routers use with reference to the devices whose design and characteristics have been described in the previous sections.Due to the unavailability of components in the laboratory with the characteristics previously described, the experimental optical bench is somewhat different from the appropriate one, but, the measurements obtained are in agreement with the calculations.
In order to carry out the measurements, the experimental lab bench showed in Fig. 8 was used; it is in agreement with the structure of Fig. 6, but, in this case, we used a reflective SLM instead of a transmissive one; therefore, it is necessary to include a polarizing beam splitter in order to direct the reflected beam to the lens.Due to the "spatial invariability" of the Fourier transform, it is not necessary to illuminate the entire SLM active surface to reproduce the diffraction pattern; taking this into account we can select, by a diaphragm aperture, the SLM zone where the incident light is focused.The characteristics of a commercial binary phase SLM are shown in Fig. 8(c).
As optical sources, a green He-Ne laser and a tunable Argon laser with g = 528.7 nm (green) and b = 462.6 nm (blue) have been used.These wavelengths have been selected because they belong to the visible spectrum and the correct alignment of the system is easier, a critical factor in the experiment.In this case, a detector-array (6.3 × 4.7 mm) of a CCD camera is placed at the "focal plane", as an image sensor, to analyze the results.A single personal computer, PC, is used to generate the CGHs for the design process described previously, and they are loaded onto the SLM by changing its pixels state; the diffracted patterns were stored in the same PC, where they could be observed and processed.To recalculate the new output fibers position, the distance for the diffraction order (x) is derived from (5) without the fixed grating: where H, defined in (4), is the hologram spatial period, but now, the maximum value for n = N/2 = 128, the size of the pixel, D =15 m and the number of pixels in one dimension of the SLM, N = 256, have been taken into account.

SLM characterization for wavelength routers
When we implement different holograms, according to n values, in the SLM and an incident light wavelength is illuminating the pixels, different diffracted angles are obtained; by placing an array of fibers at the output, in the focal plane, a -router is implemented.
To test the capability of a commercial SLM as a part of a dynamic holographic router, the holographic setup shown in Fig. 8 (a) was implemented; a photo of the experimental optical bench is shown in Fig. 8(b).For this test the optical source was an He-Ne laser at = 528.7 nm (green wavelength) and the lens focal length, 8 cm.In order to route the green wavelength to the F 4 output fiber, according to Fig. 9, it is necessary to load a CGH-(A) with a spatial period H corresponding to n = 64 in the SLM and for routing the same wavelength to the F 8 output fiber, a CGH-(B) with n = 128 was calculated and implemented onto the SLM.

SLM characterization for filters and demultiplexers
Other measurements, to test the capability of a commercial SLM as a part of a dynamic holographic device, have been done with the holographic setup shown in Fig. 8 (Alarcón, 2004).According to Fig. 9, if a CGH black & white bars type hologram with n = 128 is loaded onto the programmable SLM, a blue wavelength channel will reach the F 7 output fiber and a green wavelength channel will reach the F 8 output fiber.
The diffracted light spots distance, calculated from (9) without a fixed grating, is:  (12).Therefore, in this way, we can build an optical 1x2 demultiplexer.The central light spot is due to the zero diffraction order m = 0, with the maximum light intensity diffracted (x = 0); it can be reduced with a SLM with better performance by impacting on the total insertion losses reduction.
The temporal response of the system was also measured.The SLM optical switching time was estimated to be roughly 250 s, as the sum of the electric storage and FLC material response times (Alarcón, 2004).We also noticed a damped response when low-frequency switching is carried out; this is probably due to relaxation of the FLC molecules.

Design of equalized holographic ROADMs for application in CWDM metro networks
These type of ROADMs are designed for application in CWDM (Coarse Wavelength Division Multiplexing) networks, where the distance between the different wavelengths allow the use of DML (Direct Modulation Lasers) without cooling, reducing the cost and the tolerances of the network components.Application in METRO networks and its interconnection with some PON (Passive Optical Network), as a part of the access to the subscriber, is reviewed.Different technologies have been proposed for the implementation of ROADMs (Ma & Kuo, 2003), (Homa & Bala, 2008).Each of them has its own advantages and drawbacks.The main characteristic of holographic ROADMs is the easy way of changing the tuning and power level of the signal at the output fibers by the dynamic implementation of different holograms on the SLM according to the requirements of the network management.

Holographic ROADM structure
The working principle of the dynamic holographic device is based on the wavelength dispersion produced in a diffraction component (grating, spatial light modulator) as explained in Section 3. We use for this application a phase reflective spatial light modulator (SLM) and a fixed transmissive diffraction grating to select the corresponding output wavelength from an set of channels in the input, as shown in Fig 11 .The active element of the SLM is a Ferroelectric Liquid Crystal (FLC) with a low switching time (less than 50 s) that allows a real time operation.The role of the fixed diffraction grating is to provide more wavelength tuning range and greater total diffraction angle.

Fig. 11. Reflective holographic router
One of the reasons because we have chosen this type of "2f-folded"implementation, , is the reduced size of the device in comparison with the other possible structure, "linear-4f", where the length of the optical axis is four times the focal distance of the lens used.Its working operation has been described in Section 3.

Holographic ROADM design 8.2.1 Dynamic wavelength tuning
At the input of the router there are different wavelengths 1 , 2 ,….n according to some ITU Rec.For the design of this holographic router, these wavelengths are in agreement with the G.694 Rec. for use in CWDM systems.The range of wavelengths is from 1271 nm to 1611 nm with 20 nm as separation between channels; 4, 4+4, 8, 12 and 16 groups of channels are specified distributed along the complete range.
In a holographic router the tuning of this wavelength range is achieved by changing the spatial period of the hologram ND/n, where n is the number of pairs of bars (2-phases) or number of four bars (4-phases), N is the number of pixels and D the size of the SLM pixels.
The expression which allows the selection of the output wavelength , according to the physical parameters and structure of the device, is (Martin Minguez & Horche, 2007): where x is the distance from the optical axis to the output fiber, f is the focal length of the lens, d is the spatial period of the fixed diffraction grating and M is the number of phases.Fig. 12 shows some tuned wavelengths according to different values of n, for a typical holographic device.
Fig. 12.Four different tuned wavelengths at the output of the holographic router As we have commented in Section 4.1, for wavelengths close to the central value, the filter response is very similar to the Gauss filter; for wavelengths far from the central value, the filter response is similar to a 3 nd order Bessel filter with less out band attenuation.Both of them have a linear phase characteristic, which means a constant group delay.These simulations are in agreement with experimental measurements shown in (Parker et al.., 1998).

Holographic device losses
The losses produced in this holographic router, as we have commented before, are due to the following causes: diffraction loss: the total light diffraction is composed of the transmissive diffraction in the grating (twice) and the reflexive diffraction in the SLM.Using a 4-phases SLM and a grating with 1 st order intensity efficiency of about 80%, the total losses are 10 x log (3x.0.8) ≈ 3 dB.intrinsic SLM loss: it is due to the liquid crystal (LC) switching angle different from optimal and the coverage of SLM aperture (1/e 2 of ND x ND).A typical value is 2 dB.fibre/lens coupling: by considering 90% efficiency, 1 dB is added.In total, with an optimized holographic device, a loss about 6 dB has to be taken into account.

Channel power equalization
Power equalization at the all output channels is necessary to compensate the different response of the network components and distances for the used channel wavelengths.To reach it and to compensate for the holographic device losses, a gain component, such as a Semiconductor Optical Amplifier (SOA), has to be employed.The total equalization takes into account the gain-wavelength variation of this amplifier, ΔG A , whose typical response is drawn in Fig. 13, (the maximum gain, G A is about 20~25 dB).The target is to have at the output fibers a net loss of 0 dB (GT), according to the equation: where ΔAt is the total attenuation range for channels to be equalized at the input of the device; L HR is the intrinsic holographic router losses (≈ 6 dB) and the term ΔL HR =10 x log (number of channels) has taken into account the additional loss due to the mixed holograms utilized for equalizing all the input channels.This point will be explained in detail in the following paragraphs.Fig. 14 shows the structure of an Equalized Holographic ROADM (EH-ROADM) for 4 input channels with full routing of them to the 4 output fibers.A way to obtain at the output fibers tuned wavelengths with different relative attenuation between them is to control the losses due to the SLM aperture, as pointed out in Fig. 15.
The minimum losses due to the SLM aperture are obtained when the incident light, with a Gaussian distribution, fills the complete surface ND x ND of the SLM.Therefore, the losses are proportional to the quantity of SLM aperture illuminated by the collimated light coming from the lens, as in Fig. 15.A practical way to reach the former condition is by changing the size of the hologram according to the number of active pixels.

Mixed hologram operation
The EH-ROADM is able to select at the output fibers any combination of wavelengths at the input fiber, from all input wavelengths in just one output fiber to each input wavelength at the corresponding output fiber, including all intermediate cases.This operation mode is done by the selection in the SLM of a mixed hologram composed of all individual holograms corresponding to each input wavelength.Fig. 16 shows an example for three input wavelengths and its holograms, formed, in this case, by black and white bars (2-phases).For every input wavelength (channel) a hologram is assigned, where n i (spatial period) produces the pass-band filter for the channel and N i takes into account the number of active pixels to reach the correct attenuation, At channel , to equalize the output signals.This mixed hologram produces the additional loss in the holographic router, 10 x log (number of channels).A more fitted equalization can be obtained by monitoring the outputs with a feed-back loop to adjust the size of the holograms according to the wanted output signal level.

Design calculations
Having chosen the SLM, the focal length of the lens, f, to illuminate with collimated light the complete active surface ND x ND of the SLM (see Fig. 15), is related to the number of pixels N and their size D according to expression (8): where Φ core is the input fiber core diameter and 0 the central wavelength in the operation region.The 3 dB pass-band filter bandwidth of the device, BW, is (Parker et al., 1998) 3/2 2 0 2 if the condition 8D >> d is reached, where d is the fixed grating spatial period.For our calculations, we have a reflective 4-phases SLM with N = 1024 and D = 8 m (ND = 8.192 mm).Then, the focal distance for the lens is 37.655 mm and the BW ≥ 1.52 nm (190 GHz), d being = 6.5 m, the spatial period of a 4-phases transmissive diffraction grating and Φ = 9 m the core diameter of a singlemode fiber.By changing d we can adjust the BW of the holographic filter.
In the expression (13) the selected wavelength of operation is calculated.The value of n is varied from n = 0 (for maximum wavelength) and n = N/4 (for minimum wavelength); the central wavelength 0 is obtained when n = N/8.For the design of a 1x4 router working in the upper band of the CWDM grid, 1471-1611 nm, we take 0 = 1541 nm.In this case min = 1407 nm and max = 1693 nm; these values cover the entire CWDM upper band.The distance from the optical axis to the output fiber, (see Fig. 11), where the 1 st order of the total diffraction is produced, is x = 9.808 mm and the total diffraction angle φ ≈ 14.6º.From ITU G.694 Rec., all CWDM channels are spread Δ = 20 nm to allow Direct Modulated Lasers (DML) wavelength variation with temperature and filter tolerance; therefore, an ΔΛ = (8-1).Δ = 1611-1471 = 140 nm range assumes ΔX = 1260 m, according to the relation: In an equalized holographic router, the directing of the input wavelengths to the output fibers is done by the choice of three parameters: n ij for wavelength tuning, N i for power equalization and Δx j for placing the output optical fibers.Subscript i is related to the number of input wavelengths and subscript j related with the number of output fibers.Haqving fixed the separation between fibers, in our case Δx = 180 m, we obtain the corresponding value of n ij from ( 13), according to the input wavelength(s) and output fiber(s) considered.
As we are managing different sets of n ij values, all of them have to be different in order to avoid cross-talk between wavelengths on different output fibers.
Table 8 shows the holograms (n ij ) and number of active pixels (N i ) for a 4-channels grid according to the ITU G.695 Rec.For instance, in Fig. 11, a mixed hologram 113+95+78+61 addresses the 4 input wavelengths ( 3 + 4 + 5 + 6 ) to the output fibre 3; a mixed hologram 113+121+128+135 addresses 3 to fibre 3, 4 to fibre 4, 5 to fibre 5 and 6 to fibre 6.In each case, every i has the corresponding N i range to assure the power equalization at the output.Table 9 is a summary of the losses in the device (SOA+EH-ROADM) according to the different input channels, whose variation in wavelength is in agreement with Fig. 15.In this case, there is a net gain of 10 dB to compensate for the power variation due to different paths of the input channels along the network.The N i range, 256÷1024, in

CWDM METRO networks application
The use of tunable holographic devices in Access and Metro networks, like demultiplexers or routers has been studied in different papers (Koonen, 2006), (Martin Minguez & Horche, 2010).In Fig. 17 an application for the equalized holographic ROADM is represented.

Design of an holographic router with λ conversion and losses compensation
Fig. 18 shows a device composed of a Semiconductor Optical Amplifier (SOA) and a holographic wavelength router.The SOA performs the wavelength conversion by a non linear operation using the Cross Gain Modulation (XGM) method.An incident wavelength, i, modulated by a digital signal is combined with the wavelength CWj generated by a tunable laser (CW) into the SOA.At the amplifier output, according to different CWj wavelengths, CWj signals are obtained modulated with the digital signal from the incident i wavelength.These CWj signals are also amplified and inverted.The holographic wavelength router, depending on the input signal, CWj, , and the generated hologram (nij) stored in the SLM, addresses this signal to the assigned output.As has been stated, this technology has the drawback of high insertion losses (less than 10 dB, using an optimized device).In order to solve this problem, by combining a SOA with the holographic router, this insertion loss is compensated with the amplifier gain in the saturation zone of operation.A parameter to control in the SOA operation, is related to the amplified spontaneous emission (ASE) because of the impact on the signal distortion.Fig. 19 shows the simulation of this device, composed of three different blocks: a CW tunable laser, a wavelength conversion semiconductor optical amplifier and a wavelength holographic router.In Fig. 20, the response of the Wavelength Conversion and Routing Holographic Device (WCR-HD) is represented for a 2.5 Gb/s input signal, i = 1540 nm, which is converted to an output signal, o = 1520 nm, where the losses of the holographic router are compensated by the gain of the SOA.

Conclusion
In this chapter the design of a singular device for use both in CWDM/DWDM systems has been studied.Applications such as, tunable optical filters, demultiplexers and wavelength routers, using holographic SLM technology, have been reviewed taking into account ITU-T G.694.1 and G.694.2 Recs.for central wavelengths allocation.Application of Computed Generated Hologram design (CGH) to CWDM/DWDM systems has been studied and some comments about this hologram generation technique and its results have been made in order to highlight the phases of the process implementation and the issues related to the diffraction target misalignment and the use of 2-4 phase holograms, etc.
The novel idea in this work is the design of a compatible CWDM/DWDM device able to carry out different multiplexing functions.As we commented before, a better device performance as a tunable filter, demultiplexer or router could be implemented if only one of these functions is required.The design of equalized holographic ROADM devices for applications in CWDM optical networks has been developed.By using a mixed hologram, corresponding to the combination of several input wavelengths, the tuning of a broad range of wavelengths has been obtained allowing the full routing of several channels from the input fiber to the outputs.As it is possible to change the active pixels in the SLM for each hologram, in order to maintain a fixed output power level, channel equalization has been reached.Intrinsic losses of the device have been optimized using 4-phases holograms whose diffraction efficiency, for the 1 st order, is twice that of binary holograms.Also, the ROADM size has been minimizing by using a "2f-folded" instead of a "linear-4f" for the optical structure.To reduce the total insertion losses of the holographic device a SOA has been added increasing the input power range for equalization.An example of use of these ROADM devices in CWDM Metro and Access Networks (PONs) has been reviewed.Another example of application is dealing with the design of a holographic router with losses compensation and wavelength conversion, whose main application is in the interconnection nodes of Metro networks.This device uses a SOA (Semiconductor Optical Amplifier), in the non-linear region, to do the wavelength conversion and, in addition, to supply the gain in order to compensate for the intrinsic losses of the holographic router.
Other applications in Metro networks like path protection between nodes or switch matrix for ring networks interconnection could be implemented showing the versatility of these devices (Tibuleac & Filer, 2010).Laboratory experiments testing the capability of a phase FLC-SLM to be used in these devices have been carried out and results show that, for different types of holograms, the possibility of distributing several wavelengths depends on the diffracted angle and, therefore, enabling the building of filters, demultiplexers or wavelength routers.

Fig. 2 .
Fig. 1. two/four-phases bars holograms Fig 1 shows a bars hologram for 2 and 4-phases and their diffraction target in a far field approach.As we can see, the main difference in the holograms is the grey bars in the 4phases holograms; in this case there is a white bar, a black bar and two different grey bars for addressing the 4-phases (π/4, 3π/4, -3π/4, -π/4); with regard to the diffraction target.Another characteristic is the loss of the symmetry for the diffraction orders.

Fig. 9 .
Fig. 8. (a) Optical bench diagram; (b) experimental optical bench and c) binary phase SLM characteristics 12) where: Δ = 66.1 nm; f = 8 cm; n = 128; N = 256 and D = 15 m.In Fig.10 light spots captured by CCD camera, from the CGH with n = 128 (black and white bars) are shown.In this case the tunable Argon laser with the blue and green colors has been used.The experimental diffracted light spot distances were x blue = 1233.6µm (F 7 ) and x green = 1409.8(F 8 ) µm, separated by ∆x = 176.25 µm according to Fig. 9, in good agreement with

Fig. 15 .
Fig. 15.Losses in the incident light due to different ND x ND hologram apertures

Fig. 17 .
Fig. 17.Application of an EH_ROADM in a CWDM METRO networkA double ring CWDM METRO topology is used to connect this primary access network, through an Optical Line Termination (OLT), with some Fiber to the Office (FTTO) or Fiber to the Home (FTTH) networks with Passive Optical Network (PON) structure; on the other side, a connection to a DWDM METRO network, by an OXC (Optical Cross Connect) with conversion, is provided.The target is to address the wavelengths of the double ring network, 1 , 2 , 3 and 4 to four different PONs with the possibility of wavelength reallocation.

Fig. 18 .
Fig. 18.Device composed of an optical converter and a holographic router

Table 1 .
Relationship between phases and contrast

Table 2 .
Different device applications

Table 3
summarizes the filter figures for CWDM systems applications where channels are allocated between min = 1290 nm and max = 1590 nm, with central wavelength 0 = 1431 nm, and for DWDM systems ( min = 1530 nm and max = 1590 nm, 0 = 1551 nm).

Table 9 .
SOA gain, EH_ROADM losses and total net gain