Impact of blue filtering on effective modulation bandwidth and wide-angle operation in white LED-based VLC systems

Noha Anous; Tarek Ramadan; Mohamed Abdallah; Khalid Qaraqe; Diaa Khalil

doi:10.1364/OSAC.1.000910

1. Introduction

Visible light communications (VLC) has been recently introduced as an attractive means of communications. VLC is considered a secure, safe, energy efficient and license-free communication system solution. It is also easy to incorporate with daily illumination systems employing commercially available white light emitting diodes (LEDs). These LEDs transmit modulated light carriers, which are then demodulated by photodetectors (PDs) at the receiver [1–4]. White LEDs are available in different technologies, each of which may support a maximum data rate. Phosphor-coated LEDs, red-green-blue (RBG) LEDs, gallium nitride (GaN) micro LEDs and RGB laser support maximum data rates of 0.1, 5, 10 and 100Gbps, respectively [3]. Despite offering the lowest data rate, phosphor-coated LEDs are the most widely used white LEDs. This is due to their lower cost, less complexity in fabrication and stable luminosity against temperature variations [3–5].

Two main features are desired to be satisfied in VLC systems; (1) A large modulation bandwidth to support a high data rate system and (2) A wide-angle operation, which is to preserve the same effective modulation bandwidth under different angles of incidence (AOIs) [4,6]. In existing systems, several techniques are adopted to enhance the effective modulation bandwidth, which is the first desired feature in VLC systems. These techniques include: optical filtering to suppress the slow phosphor spectral component, analog/digital equalization for link bandwidth expansion, or using an advanced modulation technique for optimal bit/power allocation. However, wide-angle operation under such techniques has not been investigated [3,4,6–13].

According to literature, adding a blue filter before the PD at the receiver is the simplest and cheapest technique to increase transmission bandwidth, hence the most widely applied [3,4,6,8,10,14]. Blue filters provide a simple means to improve transmission bandwidth without increasing the computational complexity at the receiver (by adding post-equalization circuits for example). Hence, blue filters are considered necessary and are not preferred to be eliminated from the VLC system even if pre-equalization circuits are used [3,4,8–11]. Moreover, the application of advanced modulation techniques (such as orthogonal frequency division multiplexing OFDM) cannot be seen as an effective replacement of blue filters in a VLC system [6,7]. On the other hand, blue filters have not shown degradation in system performances despite reducing the total signal power by eliminating the yellow spectral component. According to existing literature, blue filter does not degrade VLC system performance in terms of signal-to-noise ratio (SNR) and data rate as stated in [15,16]. For example, according to the experimental work in [4], using dielectric-based blue filter with a ~100% transmission, a sharp cut-off and a wide rejection region proved an enhancement of the effective modulation bandwidth and the bit error rate of a VLC system despite the fact that the blue filter eliminates the yellow spectrum. This is mainly attributed to the fact that the wide-rejection region eliminates the ambient light noise. Hence, it is true that the signal power is degraded due to eliminating part of the spectrum, but the overall SNR is enhanced due to suppressing ambient light noise. Accordingly, the BER is enhanced as proven in [15].

In existing literature, blue dielectric filters with almost ideal transmission characteristics are considered. Such filters almost fully suppress the slow phosphor component, thus offer large effective modulation bandwidths [4,6]. However, these dielectric filters are known for their narrow-angle operation. On the other hand, plasmonic filters exhibit wide-angle operation, but may not fully eliminate the yellow phosphor component due to their non-ideal transmission characteristics [17,18]. Unfortunately, the effects of such filters on the modulation bandwidth and wide-angle operation of VLC systems have not been studied in existing literature. In this work, dielectric and plasmonic blue filters are incorporated in a VLC system employing a phosphor-coated white LED. The impact of the filters spectral characteristics on the maximum possible modulation bandwidth supported by the VLC system is investigated. The wide-angle performance under the operation of each of the filters is examined. This is achieved through synthesis of analytical expressions of the frequency response of a VLC system with a phosphor-coated white LED.

This work is organized as follows: in Section 2, necessary background information of the VLC system components are presented and frequency response of a VLC system in absence of a blue filter is given (conventional VLC system). In Section 3, conventional frequency response expressions of Section 2 are revisited in the presence of blue (dielectric and plasmonic) filters. In Section 4, numerical results are presented to assess and compare the performance of VLC systems with different blue filters (dielectric and plasmonic). VLC system performances are compared in terms of effective modulation bandwidths and wide-angle operation. Results show a trade-off between maximizing the effective modulation bandwidth and wide-angle operation of a VLC system. Hence, a figure of merit (FOM) is introduced as a means to represent such a trade-off. Moreover, empirical relations are then introduced offering a possible simple estimation of the expected modulation bandwidth at given system parameters. Discussions and justifications of the obtained results is given. A numerical example is also presented in which the optical SNR (OSNR) is quantified for VLC systems with and without a blue filter.

2. Theoretical background and VLC link model

In this section, an analytical expression of the frequency response of a VLC system employing a phosphor-coated white LED in absence of a blue filter (conventional VLC system) is illustrated. In order to step into such an expression, a concise brief on each system component of Fig. 1

Fig. 1 Block diagram of a conventional VLC system with a phosphor-coated white LED in absence of a blue filter.

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is given hereafter. Figure 1 shows a simple description of a conventional VLC system primarily discussed in this work.

2.1 Phosphor-coated white LED operation

A phosphor-coated white LED is composed of a blue LED coated with a phosphorescent yellow layer. These two colors add up to produce white light. Hence, the spectrum of the phosphor-coated LED is a combination of blue and yellow spectral components. The blue LED spectrum exhibits a peak at a wavelength of 440–460 nm with a full width half maximum (FWHM) of ~25 nm. While, the yellow spectrum, resulting from a photoluminescence process, has a peak at a longer wavelength of ~550nm and a broader spectrum with FWHM of 150nm.

The phosphor-coated white LED emission spectrum may then be expressed as the sum of the blue and yellow phosphor spectral components [6]:

S_{LED} (λ) = S_{b} (λ) + S_{y} (λ)

The above blue and yellow spectral components are associated with different radiative carrier recombination lifetimes. The recombination lifetime associated with the passive yellow (τ_y) spectrum lies in the range of 10⁻⁶–10⁻³ s whereas that of the blue spectrum (τ_b) lies in the range of 10^-9 s. Since a portion of the blue light passes through the passive phosphor layer, the slow rate of the yellow phosphor coating shall degrade the high rate of this blue LED. Consequently, the resultant (τ) increases causing a reduction of the maximum modulation bandwidth supported by the system. The effective modulation bandwidth (f_3dB) can be expressed as f_3dB = 1/(2πτ) where τ is the carrier lifetime. Thus, f_3dB is primarily limited by the long recombination lifetime of the yellow spectrum [19,20].

2.2 LED modulation process and link model

The modulation process of a phosphor-coated white LED in Fig. 1 may be described as follows [6]: the blue LED is driven by an electrical signal i_LED(t). The electrical current i_LED(t) passes through the blue LED and results in generating blue light. This process is described by an impulse response h_b(t). Similarly the impulse response of the yellow component is denoted as h_y(t).

Since one portion of the blue light is directly emitted, while the other portion passes through the slow phosphor coating as illustrated in Fig. 1. Therefore, the whole white light emission process may be described in the electrical domain as [6]:

i_{PD} (t) α i_{LED} (t) * [G_{b} h_{b} (t) + G_{y} h_{b} (t) * h_{y} (t)]

where G_b and G_b indicate the power coefficients (equivalent power gain) of the blue and yellow components, respectively (defined hereafter). The LED modulating current is i_LED(t) and the received current at the PD is i_PD(t). It is important to note that the optical-to-electrical and the electrical-to-optical conversions are included in Eq. (2). Equation (2) is written in the electrical domain.

The impulse responses of the blue LED and the slow yellow phosphor components may be expressed by a decaying exponential function [21,22]:

h_{b} (t) = \frac{1}{τ_{b}} u (t) \exp (- t / τ_{b})

h_{y} (t) = \frac{1}{τ_{y}} u (t) \exp (- t / τ_{y})

where u(t) is the unit step function and τ_b, τ_y are the carrier recombination lifetimes of blue and yellow components, respectively. Hence, the frequency response of Eqs. (3a) and (3b) may be expressed as:

H_{b} (f) = 1 / [1 + j 2 π f τ_{b}]

H_{y} (f) = 1 / [1 + j 2 π f τ_{y}]

And consequently, the frequency response of the link described in Eq. (2) takes the form [6]:

H (f) = \frac{1}{1 + j 2 π f τ_{b}} (G_{b} + G_{y} \frac{1}{1 + j 2 π f τ_{y}})

To thoroughly study Eq. (5), G_b and G_b need to be calculated as shown hereafter. As for the carrier lifetimes τ_b and τ_y, typical measured values are adopted throughout this work as described in Section 4. This allows obtaining realistic VLC system evaluation when employing different architectures of blue filters.

2.3 Effective PD responsivity

The wavelength dependent responsivity of the PD is denoted herein by R(λ). R(λ) is the actual spectral behaviour of the PD. An effective PD responsivity may be defined as R_eff = R_b + R_y; where R_b and R_y are the effective responsivities of each of the blue and yellow spectra, respectively. Effective responsivities aim to describe how the PD responses to the specific blue and yellow spectra of a specific phosphor-coated white LED. Hence, the effect of the PD responsivity behaviour among with the spectral behaviour of the white LED are embodied in the effective responsivities of blue and yellow spectra, respectively [6]:

R_{b} = \frac{1}{P_{w}} \int_{Blue Spectrum} S_{b} (λ) R (λ) d λ

R_{y} = \frac{1}{P_{w}} \int_{Yellow Spectrum} S_{y} (λ) R (λ) d λ

where

P_{w} = \int_{380 nm}^{720 nm} S_{LED} (λ) d λ

is the power calculated from the emission spectrum of the phosphor-coated white LED. P_w is not the actual LED power.

2.4 Power gain coefficients

The power coefficients G_b and G_b are defined as the equivalent gains of the blue and yellow components, respectively. They are calculated by taking into account the LED emission spectrum S_LED from Eq. (1), the PD responsivity in addition to the blue filter transmission characteristics. Blue and yellow power gain coefficients may be defined as:

G_{b} = P \frac{R_{b}}{{R^{'}}_{b}}

G_{y} = P \frac{R_{y}}{{R^{'}}_{y}}

where R_b and R_y are as previously defined in Eqs. (6a) and (6b), and R'_b and R'_y are the blue and yellow spectral densities from the LED source and are defined as:

{R^{'}}_{b} = \frac{1}{P_{w}} \int_{Blue} S_{b} (λ) d λ

and

{R^{'}}_{y} = \frac{1}{P_{w}} \int_{Yellow} S_{y} (λ) d λ

. The power of the optical signal incident on the PD (P) is given by [6]:

P = \frac{P_{w}}{Φ} E_{ν} A

where P_w is the power calculated from the emission spectrum as previously illustrated. Φ is the luminous function given by [23,24]:

Φ = 683 \int_{380 nm}^{720 nm} S_{LED} (λ) V (λ) d λ

with V(λ) defined as the visibility of the human eye and values are extracted from [25]. E_v is the illuminance in lux (lx) and A is the area of the PD. Values for E_v and A are mentioned hereafter.

3. Blue filtering effect

The effect of the reduced modulation bandwidth resulting from the slow phosphor component in phosphor-coated white LEDs can be alleviated. This may be done by modulating the blue light from the LEDs at a higher rate and eliminating the slow yellow component using a blue light transmission filter at the receiver as shown in Fig. 2

Fig. 2 Block diagram of a VLC system with a phosphor-coated white LED and a blue filter.

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[3,4,6,11]. The VLC system in Fig. 2 is the same as that in Fig. 1, but with a blue filter placed in front of the PD. Clearly, the efficiency of this remedy (adding a blue filter) depends on the selectivity of the filter and its ability to suppress the yellow component of light in addition to other ambient noise components [4,17].

Satisfying high blue filter selectivity is not a trivial task because the emission peaks of blue and yellow light are relatively close with the yellow component exhibiting a relatively wide bandwidth as seen in Fig. 3

Fig. 3 Spectral characteristics of MCWHL5 phosphor-coated white LED and DET10A Si-based PD, respectively. Data used to plot the curves is extracted from [27] and [28], respectively.

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. Moreover, a high performance filter requires a wide rejection region (till 1050nm) to reduce ambient light noise such as sunlight, lights from surrounding fluorescent and incandescent lamps among other light sources that may be present in the background [3,4,6]. The value of 1050nm is typically the maximum wavelength in the response spectrum of silicon (Si) detectors most commonly used in VLC systems [4]. In this work, employing different blue filters (dielectric and plasmonic) to a VLC system will be assessed in order to demonstrate how placing a blue filter before the PD may alter the maximum possible modulation bandwidth supported by a VLC system.

Equations (6a) and (6b) describe how the PD receives the blue and yellow spectral parts, respectively based on the LED spectral characteristics and the PD responsivity. If a blue filteris added at the receiver, before the PD, then the transmission characteristics of the filter [T_Filter(λ)] will certainly affect R_b and R_y. Hence, to account for the blue filter effect, Eqs. (6a) and (6b) may be re-written as:

R_{b} = \frac{1}{P_{w}} \int_{Blue Spectrum} S_{b} (λ) T_{Filter} (λ) R (λ) d λ

R_{y} = \frac{1}{P_{w}} \int_{Yellow Spectrum} S_{y} (λ) T_{Filter} R (λ) d λ

Thus, resulting in an effective PD responsivity given by:

R_{eff} = R_{b} + R_{y}

Equivalent power gain coefficients, G_b and G_y, in case of adding a blue filter are to be computed from Eqs. (7a) and (7b) R_b and R_y definitions as given by Eqs. (9a) and (9b). The equivalent frequency response of such a VLC system is still represented by Eq. (5) but using the above modified definitions that include the effect of the added blue filter.

In this work, the impacts of dielectric and plasmonic blue filters exhibiting different T_Filter(λ) are studied. Blue dielectric filters offer almost ideal transmission characteristics through utilizing a large number of high and low index alternating layers [4,6,14]. Such filters almost fully eliminate the slow phosphor component, thus offer large effective modulation bandwidths [4,6]. However, these dielectric filters suffer from a narrow-angle operation. On the other hand, plasmonic filters offer wide-angle operation, but may not fully suppress the yellow phosphor component due to non-ideal transmission characteristics [17,18]. Without loss of generality, an example of each is assessed in this study. The first (Filter I) is an all-dielectric blue filter adopted from [4]. It is a 120 layer multi-cavity-based filter that exhibits a box-like transmission passband with a sharp cut-off wavelength at approximately the edge between blue and yellow spectra. On the other hand, the second filter (Filter II) is a hybrid plasmonic 5 layer blue filter adopted from [17]. Although it does not exhibit a sharp cut-off edge, it outperforms the first filter in manifesting a transmission behaviour that is angle-tolerant and robust against possible fabrication errors. The detailed architectures and differences between the above two filters are given in Table 1

Table 1. Architectures of Filter I and II Used in this Work Adopted from [4] and [17], Respectively

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and their transmission behaviours are demonstrated in Fig. 4(a)

Fig. 4 (a) (left) Transmission characteristics of dielectric and plasmonic Filters I [4] and II [17], respectively at normal incidence and AOI = 50°. Generated from characteristic matrix approach of Abeles [29] using MATLAB, (b) (right) Emittance and reception angles definitions. Reception angle is denoted throughout this work by the angle of incidence (AOI).

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. Materials used in the dielectric filter are tantalum penta-oxide (Ta₂O₅) and silicon dioxide (SiO₂), while those of the plasmonic filter are titanium dioxide (TiO₂) and silver (Ag). Both filters are deposited on a fused silica substrate [4], [17].

In Fig. 4(a), the transmission of dielectric and plasmonic Filters I and II are demonstrated for AOI of 0° and 50°, respectively. AOI herein are defined as the angle between the incident light ray and normal on the receiver’s plane as shown in Fig. 4(b). Dielectric Filter I shows a shifted transmission to shorter wavelengths as AOI increases. This is a typical behaviour expected from most dielectric multi-cavity filters [26]. This blue shift in the filter’s transmission characteristics affects the amount of blue spectral power passing through it. On the other hand, plasmonic Filter II shows an angle tolerant transmission behaviour. Angle tolerance herein may be explained in the sense of the filter’s ability to preserve its spectral transmission characteristics at different AOI.

Although plasmonic Filter II achieves angle tolerance till ~50°, it clearly suffers from a lower transmission and a non-sharp cut-off behaviour when compared to dielectric Filter I. These variations in behaviours are expected to impose limitations to the VLC system in which the filters are used. This study is dedicated to exploring such limitations and results are shown hereafter.

4. Results and discussion

This work studies the impact of blue filters on maximizing the effective f_3dB of a VLC system employing a phosphor-coated white LED under wide-angle operation. The system components of the VLC system of interest in this work are as shown in Fig. 2 and Table 2

Table 2. VLC System Components of Fig. 1 and Fig. 2

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. To do this study and obtain realistic results, actual VLC component parameters are adopted. In this work, and without loss of generality, the VLC system under study employs specific commercial components in addition to blue filters from existing literature as given in Tables 1 and 2. For the white LED, typical values of 16ns and 62ns for τ_b and τ_y, respectively, are used [6]. The maximum illuminance E_v is 16988 lx [27]. As for the PD, the active area A is 0.8mm² [28].

The transmission performances and results in this work are generated by applying the characteristic matrix approach of Abeles [29]. The design of the plasmonic filter is optimized using OpenFilter software [17,30] while all other results are generated using Matlab. Dielectric constants of materials in this work are extracted from [31]. Equations (1) through Eqs. (9a) and (9b) are used to calculate f_3dB under different AOI and blue filter architectures.

The above equations are partially adopted from [6] with some modifications to account for the blue filtering effect. Thus, it is essential to point out the differences between [6] and this work. Reference [6] studies the impact of blue filtering on three actual modulation formats. The blue filter in [6] is assumed to be ideal filter (i.e. with 100% transmission and sharp edged at the blue-yellow edge). The study does not include wide-angle performance of the VLC system.

Moreover, a linear approximation of the PD responsivity is used to generate the results. On the other hand the work herein studies the impact of two different blue filter architectures; dielectric and plasmonic on the wide-angle performance of a VLC system employing white phosphorous LED. The wide-angle performance of the VLC system is assessed when using each of the two filters. The filters transmission characteristics are not ideal as assumed in [6]. Off-the-shelf LED and PD data are used to generate the results. Results show performance dependence on the PD responsivity. Hence, the main difference between this work and [6] is that we investigate the relation between f_3dB and the wide-angle performance of a VLC system using dielectric and plasmonic-based blue filters, which is not at all the scope of [6]. Through this analysis we have reached a trade-off relation and we have presented a FOM and an empirical formula to find f_3dB.

In this section, we will first study the effect of dielectric and plasmonic blue filters of Table 1 on the VLC system in Fig. 2 at normal incidence (subsection 4.1). This is followed by an investigation of the system performance under wide-angle operation for each of the two filters (subsection 4.2). The effects of the transmission characteristics of the filters on f_3dB are also demonstrated and justified (subsection 4.3). A figure of merit (FOM) is then proposed for a more adequate representation of the system performance under different blue filters (subsection 4.4). Then, empirical relations are introduced as a simple means to quantify f_3dB in case of dielectric and plasmonic filters (subsection 4.5). Finally, a numerical example is presented where a LOS VLC scenario is studied with calculations to the OSNR with and without the blue filter insertion (subsection 4.6).

4.1 Upper and lower bounds of modulation bandwidths

The upper and lower bounds of the modulation bandwidths are determined by the frequency response behaviour of the blue and yellow spectral components of the white LED, respectively. Figure 5(a)

Fig. 5 The effect of dielectric and plasmonic Filters I and II on the maximum possible modulation bandwidth at normal incidence (AOI = 0°). Generated using Eqs. (4) and (5): (a) (left) For warm LED, (b) (right) employing LEDs with different white shades [27,32,33] along with each of dielectric and plasmonic blue filters.

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demonstrates the normalized frequency response; i.e., normalized H(f) for the VLC system in Fig. 1 and Fig. 2 with system components given in Tables 1 and 2. H(f) herein is calculated from Eqs. (5) through (10). The blue solid and the yellow dashed curves are the normalized H(f) of the blue LED and the phosphor component, as calculated from Eqs. (4a) and (4b), respectively. These two curves set the upper and lower possible bounds of the effective modulation bandwidth (f_3dB) supported by the above VLC system. It is clear that the yellow phosphor component is responsible for the lower bound of f_3dB due to its large recombination lifetime as previously illustrated. Hence, placing a blue filter to eliminate this slow component contributes to increasing the f_3dB supported by the system [4,6,11]. The phosphor yellow spectral component begins to appear at λ~479nm as seen in Fig. 3. Thus, a filter that totally cuts out the yellow spectrum is expected to result in a higher f_3dB. This is clear in Fig. 5(a). Since dielectric Filter I exhibits a box-like transmission performance with a sharp edge at ~488.5nm, it eliminates a larger portion of the yellow spectrum than plasmonic Filter II. Consequently, a larger f_3dB may be supported by the above VLC system when employing dielectric Filter I.

Effective modulation frequency f_3dB is computed for different shades of white light LEDs when employing dielectric and plasmonic filters. Cold, neutral and warm LEDs used are MCWHL5 [27], MNWHL4 [32] and MWWHL4 [33], respectively. Equivalent H(f) are plotted in Fig. 5(b). The system behaviour in terms of its frequency response seems to be similar in the three cases. However, warm white LED may exhibit slightly a better performance due to having the blue-yellow edge at a slightly higher value (482nm instead of 479nm for neutral and warm white LEDs). For this reason, the filter cut-off – which is ~488.5nm passes less amount of yellow spectrum compared to cold and neutral white LEDs. Without loss of generality, the upcoming results are generated using cold white LED of [27]. Despite the importance of supporting a large f_3dB, there exists another challenge to fulfil. That is to perceive the same modulation bandwidth consistently under different AOI (wide-angle performance). This aspect is quite of interest to guarantee a consistent performance under different transmitter/receiver rotations. Wide-angle performance of the above VLC system is discussed hereafter.

4.2 Wide-angle performance

The wide-angle performance of the VLC system in Fig. 2 is evaluated in Fig. 6 and 7

Fig. 6 (a) (left) Normalized H(f) when using Filter II under different AOI. Generated using Eqs. (4) and (5). Curves with the same colors in Fig. 6(a) are reproduced from Fig. 5(a), (b) (right) Cut-off wavelength (λ_cf) of Filters I and II, respectively at different AOI [17].

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Fig. 7 R_y/R_b for filter I and II, respectively at different AOI. Generated using Eqs. (9a) and (9b).

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. The effect of changing the AOI on the previously illustrated VLC system employing plasmonic Filter II is shown in Fig. 6(a). The AOI is varied from 0°-60° and equivalent normalized H(f) values are computed. At different AOI, the system exhibits almost the same response as seen in Fig. 6(a). The inset of Fig. 6(a) shows very slight shifts in f_3dB as AOI changes. The maximum shift experienced by f_3dB is 0.5% at an AOI of 60° compared to that at 0°. Hence Fig. 6(a) verifies the possibility of a wide-angle performance of a VLC system employing a plasmonic angle tolerant filter such as Filter II.

It is observed from Fig. 6(a) that f_3dB slightly increases as AOI increases for AOI less than 50°. As AOI further increases, f_3dBshows a decrease in its value. Although the variation of f_3dB is less than 0.5% of its value at 0°, it is important to justify the above behaviour. This may be explained in the light of Fig. 6(b). Figure 6(b) shows the cut-off wavelengths (λ_cf) at different AOI for dielectric and plasmonic Filters I and II, respectively. The horizontal line indicates the border of the blue spectrum, which mostly lies between 475 and 485nm (see Fig. 3). To guarantee a reliable operation of the VLC system, λ_cf is required to stay above the horizontal line in Fig. 6(b). This is because when λ_cf drops below the edge of the blue spectrum, this indicates partial loss of the blue spectrum initially sent by the white LED. For AOI less than 50°, the blue plasmonic Filter II eliminates a portion of the yellow spectrum. This eliminated portion increases as AOI increases due to a blue shift in Filter II cut-off as seen in Fig. 6(b). At angles beyond 50°, λ_cf falls significantly below the horizontal line in Fig. 6(b). This indicates that the blue shift in plasmonic Filter II transmission causes an elimination of a part of the blue spectrum as well in addition to the eliminated yellow spectrum. This occurs to dielectric Filter I at a much lower AOI value, which manifests the wide-angle performance of plasmonic Filter II in comparison to dielectric Filter I.

It follows from the above discussion that λ_cf of the blue filter affects f_3dB through determining the portions of blue and yellow spectra reaching to the PD. However, λ_cf is not the only player, the maximum transmission of the filter also contributes in the blue and yellow responsivities as given by Eqs. (9a) and (9b). The ratio R_y/R_b, which shows the amount of yellow spectrum to blue spectrum reaching the receiver after passing through the filter and the PD. R_y/R_b is calculated from Eqs. (9a) and (9b) and plotted in Fig. 7 against different AOI for dielectric and plasmonic Filters I and II, respectively. Results from Fig. 7 may be interpreted in the light of two regions; for AOIs equivalent to λ < λ_cf and AOI equivalent to λ > λ_cf [see Fig. 6(b)]. In the first region, for dielectric Filter I, the R_y/R_b ratio exhibits a value that is only ~10.5% of that achieved by plasmonic Filter II. This may be attributed to two reasons: 1) The difference in maximum transmissions of Filters I and II, which is 98% and 79%, respectively. This results in a less amount of R_b in case of Filter II) the sharp edge of Filter I compared to that of Filter II. The slow roll-off of Filter II allows the passage of a relatively significant portion of yellow light through the filter which contributes to a relatively higher R_y in case of Filter II. Combining these two reasons, R_y/R_b ratio is expected to have larger values in case of applying Filter II. It is important to note that as AOI increases, and due to blue shifts in the spectral transmissions of both filters as indicated by Fig. 4(a) and Fig. 6(b), a slightly smaller yellow portion passes through both filters. This reflects in Fig. 7 as a decreased R_y/R_b ratio at increased AOI. The value R_y/R_b reaches zero for Filter I at an AOI of ~24°, which is equivalent to λ_cf = 474.5nm. At this angle, λ_cf coincides with the blue-yellow spectral edge [red horizontal line in Fig. 6(b)]. Hence, at AOI = 24°, Filter I allows only the passage of the blue spectrum with a complete rejection of the yellow spectral component (R_y = 0). On the other hand, in the second region, values of R_y/R_b beyond AOI where λ_cf falls below 474.5nm behave differently. At these values, the blue spectrum will be partially transmitted which does not guarantee proper operation of the VLC system [4,6]. Moreover, for dielectric Filter I, some transmission peaks begin to appear in the yellow spectral region, hence an increase in R_y is expected. Along with the expected drop in the value of R_b, this causes the increase in R_y/R_b in Fig. 7 at large AOI. Plasmonic Filter II on the other hand shows a consistent R_y/R_b ratio over a wide range of AOI, which is expected from an angle-tolerance.

To summarize, it is evident from Fig. 5 through Fig. 7 that the effective modulation frequency is affected by the R_y/R_b ratio, which in turn is affected by the value of λ_cf of the employed blue filter. The dielectric Filter I shows a higher f_3dB than plasmonic Filter II at lower AOI due to lower R_y/R_b values. Lower R_y/R_b values are due to the sharp cut-off in Filter I transmission characteristics. On the other hand, plasmonic Filter II exhibits a wide-angle behaviour, which reflects from approximately same R_y/R_b ratio for all AOI.

4.3 Blue filters effect on f_3dB

In Fig. 8(a)

Fig. 8 (a) (left) Relative responsivities of dielectric and plasmonic Filters I and II, under operating a VLC system of Fig. 2 with actual PD of Fig. 3. Generated using Eqs. (9a), (9b), ${R^{'}}_{b} = \frac{1}{P_{w}} \int_{Blue} S_{b} (λ) d λ$ and ${R^{'}}_{y} = \frac{1}{P_{w}} \int_{Yellow} S_{y} (λ) d λ$ , (b) (right) Maximum modulation bandwidth for dielectric and plasmonic Filters I and II, respectively when operating with an actual PD of Fig. 3. Values of f_3dB in case of plasmonic filter are extracted from Fig. 6(a) [Eq. (5) at different AOI]. Similarly, for f_3dB in case of dielectric filter, but the Fig. is omitted to avoid redundancy.

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, the amounts of blue and yellow spectra reaching the receiver (R_b,y) with respect to those coming out from the LED (R'_b,y) are plotted versus different AOI for dielectric and plasmonic Filters I and II of Table 1. These amounts are defined herein as relative responsivities and denoted by R_b/R'_b and R_y/R'_y. As illustrated in Fig. 6(b) and Fig. 7, dielectric Filter I is expected to achieve higher and lower values of R_b and R_y, respectively when compared to plasmonic Filter II. The effect of the PD responsivity in Fig. 3 is included in calculations of R_b and R_y as given by Eqs. (9a) and (9b). The PD behaviour in Fig. 3 shows a higher responsivity at the yellow spectrum when compared to the blue spectrum. However, this PD response has a minor impact in the case of dielectric Filter I since the amount of received yellow spectrum is minimal. The prominent impact of such PD responsivity appears when a relatively significant amount of yellow light is received as in the case of plasmonic Filter II. This relatively significant amount is further magnified by the increased PD responsivity in the yellow spectrum, causing an increase in R_y/R'_y, which in turn causes a decrease in the maximum f_3dB following Eq. (5). Beyond AOI of 45°, R_b/R'_b for dielectric Filter I shows a massive decrease when compared to that of plasmonic Filter II. This is due to the aforementioned reason of decreased amount of blue light reaching the PD due to angle intolerant behaviour of dielectric Filter I.

The effect of the filters transmission characteristics along with the PD responsivity on f_3dB is shown in Fig. 8(b). The upper and lower bounds of f_3dB are plotted as horizontal dotted-dashed lines in Fig. 8(b). When applying dielectric Filter I, f_3dB experiences a maximum possible value of 16.5-17 MHz, in contrast to ~12.13–12.58MHz in case of applying plasmonic Filter II, under the same PD employment. This may be explained in terms of results in Fig. 7, Fig. 8(a) and Eq. (5). According to Eq. (5), H(f) behaviour is not only affected by the amount of blue spectrum reaching the receiver but also with R_y/R_b. The slight increase in f_3dB in case of dielectric Filter I or plasmonic Filter II as AOI increases is due to the blue shift in the transmission characteristics as previously explained. This blue shift results in passing a less amount of the undesired yellow spectrum as shown in Fig. 4(a) and Fig. 6(b).

Again, it is important to recall the angle tolerant behaviour capability of both filters. A trade-off is observed between the effective f_3dB and its consistency over a large range of AOI. Plasmonic Filter II offers a maximum f_3dB that is less than that offered by dielectric Filter I by ~26%. However, plasmonic Filter II continues to operate consistently under higher AOI. The importance of high transmission, box-like, and angle tolerant filter combined behaviour appears from Fig. 8(b), where operation with a maximum f_3dB is possible under a wide range of AOI. To indicate the severity of this trade-off a figure of merit (FOM) is introduced hereafter.

4.4 Figure of merit (FOM)

It is important to note that neither Fig. 6(b) nor Fig. 8(b) alone may be used to evaluate the performance of a VLC system employing dielectric and plasmonic filters. A combination of the results in both Figures is needed to quantify not only that the yellow component is eliminated, but also the amount of blue light transmitted through the filter. For example in the case of dielectric Filter I, a smaller value of R_b/R'_b is seen at AOI = 50° in Fig. 8(a) which agrees with Fig. 6(b) in which λ_cf~430nm. This indicates that almost half of the blue light does not pass through the filter. But observing Fig. 8(b), it is seen that at 50°, f_3dB still preserves its large value. Hence a FOM is needed to evaluate the effect of the blue filters on not only the f_3dB, but also the amount of blue spectral power reaching the PD.

The proposed FOM is defined as FOM = f_3dB × R_b/R'_b. The larger the FOM, the larger the f_3dB supported by the VLC system will be. The FOM is computed when employing both dielectric and plasmonic Filters I and II and plotted in Fig. 9

Fig. 9 FOM to measure the effect of dielectric and plasmonic filters on the VLC system performance. Values of R_b/R'_b and f_3dB are extracted from Fig. 8(a) and 8(b), respectively.

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. The dielectric Filter I with a box-like transmission shows a better performance that continues to ~40°. On the other hand, the plasmonic filter shows a consistent lower performance till ~70°.

4.5 Averaging effect

It is interesting to observe that inserting a blue filter before the PD in a VLC system employing phosphor-coated white LEDS, results in an averaging effect as might be called. The value of effective f_3dB may be graphically computed from plotting Eq. (5) as in Fig. 6(a). However analytical estimation requires a trial and error procedure.

An empirical relation may be deduced expressing the resulting effective f_3dB as a weighted average between f_3dB-Blue and f_3dB-Yellow. The values f_3dB-Blue and f_3dB-Yellow are the 3dB modulation bandwidths of the blue LED and yellow spectral component as computed from Eqs. (4a) and (4b), respectively. The weighting constants are R_b and R_y as computed from Eqs. (9a) and (9b). The empirical relation may be given by:

f_{3 dB} = \frac{R_{b} f_{3 dB-Blue} + R_{y} f_{3 dB-Yellow}}{R_{eff}}

where R_b, R_y, and R_eff are given by Eqs. (9) and (10). The 3dB bandwidths, f_3dB-Blue and f_3dB-Yellow are the inverse of blue and yellow recombination lifetimes; τ_b and τ_y, respectively.

In Fig. 10

Fig. 10 The effect of dielectric and plasmonic filters I and II along with the PD responsivity on the maximum possible modulation bandwidth f_3dB along with empirical relation results comparison. Curves with the same colors in Fig. 10 are reproduced from Fig. 8(b).

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, f_3dB-Blue and f_3dB-Yellow are indicated by upper blue and lower yellow dotted–dashed lines. The computed f_3dB that follows from Eq. (5) is compared to that calculated by the empirical relation given by Eq. (11). The deduced relation in Eq. (11) shows a very good approximation in the case of Filters I and II with an overestimation estimation error in case of Filter II. The overestimation seems to be due to a constant factor that may be missing. A multiplication factor is hence needed in case of plasmonic filters. Another empirical formula with a more profound effect of the yellow spectrum can thus be expressed as:

f_{3 dB} = \frac{R_{b} f_{3 dB-Blue} (1 - \frac{R_{b}}{{R^{'}}_{b}}) + R_{y} f_{3 dB-Yellow} (1 - \frac{R_{y}}{{R^{'}}_{y}})}{R_{eff}}

Equation (12) is more accurate in case of non-ideal filters such as Filter II, whereas Eq. (11) gives a better estimation in the case of box-like transmission filters. The above relations offer a simple estimation of the system’s maximum modulation bandwidth if the employed white LED, PD and filter’s spectral responses are known.

4.6 Numerical example and OSNR

A numerical example is given herein for more illustration and insights into the above mentioned results. The VLC system in Fig. 1 and Fig. 2 are considered. The VLC channel is assumed as a LOS free space link. Consider a point source emitter and receiver, the VLC LOS channel gain may be defined in terms of the distance between transmitter and receiver d_i as well as the angle dependent transmitter and receiver functions [34]:

H_{LOS} = G_{TX} (φ) G_{RX} (ψ) / d_{i}^{2}

where φ and ψ are the angles of emittance and reception as shown in Fig. 4(b). φ and ψ are measured from the emitted ray of light to the normal on the transmitter/receiver planes, respectively [34]. Since, most LEDs emit a Lambertian transmission cone, then G_TX(φ) may be written as:

G_{TX} (φ) = \frac{m + 1}{2 π} \cos^{m} (φ)

where m = −ln(2)/ln(cos(Φ_1/2)) is the Lambertian order with Φ_1/2 is the semi-angle at half power. Assuming concentrator optics at the receiver, G_RX(ψ) may be expressed as:

G_{RX} (ψ) = A g (ψ) \cos (ψ)

where A is the PD area and g(ψ) is the gain of a non-imaging hemispherical concentrator with an internal refractive index n and a field of view FOV of Ψ_c such that:

g (ψ) = {\begin{matrix} \frac{n^{2}}{\sin^{2} (Ψ_{c})} & 0 \leq ψ \leq Ψ_{c} \\ 0 & ψ > Ψ_{c} \end{matrix}

In this work, g(ψ) is set to unity for 0 ≤ ψ ≤ Ψ_c and zero otherwise. Hence, the received power at the PD may be written as P_RX = H_LOSP_TX [34], hence P_RX may be written as:

P_{RX} = \int_{Visible Spectrum} S_{LED} (λ) T_{Filter} (λ) H_{LOS} d λ

where T_Filter(λ) denotes the spectral transmission characteristics of the blue filter used. In case of the VLC system in Fig. 1, T_Filter(λ) is simply set to unity.

As previously mentioned, one important benefit of adding a blue filter with a wide rejection region is to suppress the ambient noise resulting from sunlight, fluorescent, incandescent and halogen lamps [4]. Total ambient noise power may be calculated by:

N = \int_{Visible Spectrum} S_{N} (λ) d λ

where S_N(λ) is the spectral distribution of ambient noise as shown in Fig. 11

Fig. 11 Sunlight and fluorescent lamps spectra used as ambient noise spectra in Eq. (19). Spectra extracted from [35].

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[35]. In this numerical example, sunlight (from windows) and fluorescent lights (indoor lights) are to be considered as ambient noises. Equation (18a) calculates the noise power in case of absence of a blue filter. When a blue filter is added, Eq. (18a) may be written as:

N_{f} = \int_{Visible Spectrum} S_{N} (λ) T_{Filter} (λ) d λ

where N_f denotes the filtered ambient noise. From Eqs. (17) and (18), a ratio between the received power at the PD and the noise power may be defined as the OSNR ratio for the VLC systems in Fig. 1. It may be quantified by [36]:

O S N R (dB) = 10 \log (P_{R X} / N) + 10 \log (B_{m} / B_{r})

where B_m is the equivalent noise bandwidth and B_r is the reference optical bandwidth usually assumed as 0.1nm. For the VLC system in Fig. 2, the OSNR shall be denoted by OSNR_f. It is also computed by Eq. (19) by replacing each N with N_f, which is the noise after the blue filter.

In Fig. 12

Fig. 12 OSNR versus AOI for VLC systems in Fig. 1 and Fig. 2. OSNR and OSNR_f are computed using Eq. (19).

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, OSNR and OSNR_f from Eq. (19) are calculated and compared for the VLC systems in Fig. 1(without blue filter) and Fig. 2 (with blue filter), respectively. System and channel parameters are as given in Table 2. The effect of applying a blue filter with a wide rejection region is obvious in Fig. 12. An enhancement of ~31% in the OSNR is achieved after inserting the blue filter. The filter suppresses a significant portion of the ambient noise. Although the filter degrades the signal power, this is compensated by significantly decreasing the noise power. The sharp cut-off of the dielectric filter allows for a better performance at lower AOI. However, the plasmonic filter results in a higher OSNR at larger AOI. The importance of plasmonic blue filter lies also in effectively extending the receiver’s FOV. For the system in Fig. 1 (no blue filter), the receiver fails to receive signals coming at angles beyond the FOV (60°). Whereas when using a plasmonic blue filter, the OSNR is degraded due to path loss, but effectively a signal may be received. In this example the values of OSNR are relatively small. In practice a concentrator or an amplifier may be used to enhance OSNR.

Figure 13

Fig. 13 FOM and OSNR_f for The VLC system in Fig. 2 when using a dielectric and plasmonic filters, respectively. FOM curves (upper two curves) are reproduced from Fig. 9. OSNR_f computed using Eq. (19).

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shows the OSNR_f in relation to the FOM previously discussed in Fig. 9. It is seen that the FOM follows a similar behaviour to the OSNR_f curves. This shows that the FOM introduced in this work is a good indicator of the system performance. Practical values of FOM depend on the LED source, blue filter, and PD responsivity.

5. Conclusion

This work studies the impact of two distinct blue filter transmission characteristics on the maximum effective modulation bandwidth (f_3dB) of a VLC system with a phosphor-coated white LED. Two different filters are considered: a 120 layers dielectric filter with nearly box-like response and an angle-tolerant plasmonic filter. The f_3dB is calculated for the VLC system with commercial white LED and PD and the above blue filters which are extracted from literature. The impact of ideal and non-ideal angle-tolerant transmission blue filters at the receiver are examined. The ability of the filter in rejecting the undesired yellow spectral component directly affects the maximum effective f_3dB of the system. The non-ideal filter with a slow roll-off (plasmonic filter) results in a larger yellow to blue responsivity ratio (R_y/R_b) than that with a high transmission box-liked spectral characteristics of a dielectric filter. Hence, an f_3dB in the case of the plasmonic filter in this study is less by ~26% than in the case of the dielectric filter. However, the larger value of f_3dB when using a dielectric filter comes at the expense of narrow-angle operation in contrast to a wider-angle operation in case of the plasmonic filter in this study. A trade-off thus exists between obtaining a high value of f_3dB and a wide-angle performance simultaneously. This trade-off is represented by a FOM. Moreover, the blue filter impact is introduced as an averaging effect to the maximum possible modulation bandwidth supported by the system. This averaging effect depends on the filter characteristics in addition to the PD responsivity. An empirical formula for effective f_3dB as a weighted average of the blue and yellow light components in the system is thus proposed. A numerical example is presented where the OSNR is calculated in VLC systems with and without the insertion of a blue filter. OSNR is enhanced when a blue filter with a wide rejection region is used due to rejection of ambient noise.

Funding

NPRP award [NPRP 9-077-2-036] from the Qatar National Research Fund (a member of the Qatar Foundation).

Acknowledgment

This work was made possible by the NPRP award [NPRP 9-077-2-036] from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the author[s].

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10. C. H. Yeh, C. W. Chow, Y. L. Liu, H. Y. Chen, Y. Liu, and J. C. Hsu, “Investigation of no analogue-equalization and blue filter for 185 Mbps phosphor-LED wireless communication,” Opt. Quantum Electron. 47(7), 1991–1997 (2015). [CrossRef]

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12. C. Chen, W. Zhong, and D. Wu, “Indoor OFDM visible light communications employing adaptive digital pre-frequency domain equalization,” in 2016 Conference on Lasers and Electro-Optics (CLEO), San Jose, CA (2016), pp. 1–2 .

13. H. Chun, A. Gomez, G. Faulkner, and D. O’Brien, “A spectrally efficient equalization technique for optical sources with direct modulation,” Opt. Lett. 43(11), 2708–2711 (2018). [CrossRef] [PubMed]

14. H. Chun, S. Rajbhandari, G. Faulkner, and D. O’Brien, “Effectiveness of blue-filtering in WLED based indoor visible light communication,” in Proc. of IEEE 3rd Int. Workshop Opt. Wireless Commun. (2014), pp. 60–64.

15. J. Y. Sung, C. W. Chow, and C. H. Yeh, “Is blue optical filter necessary in high speed phosphor-based white light LED visible light communications?” Opt. Express 22(17), 20646–20651 (2014). [CrossRef] [PubMed]

16. H. Li, Y. Zhang, X. Chen, C. Wu, J. Guo, Z. Gao, W. Pei, and H. Chen, “682 Mbit/s phosphorescent white LED visible light communications utilizing analog equalized 16QAM-OFDM modulation without blue filter,” Opt. Commun. 354, 107–111 (2015). [CrossRef]

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	Structure	T_max (dB)	λ_Cut-off (nm)	Angle tolerance
Dielectric Filter I [4]	120 layers all-dielectric filter: Substrate\|1.8 (0.5LH 0.5L) ^∧15 1.5(0.5LH 0.5L) ^∧15 1.2(0.5LH 0.5L) ^∧15 (0.5L H 0.5L) ^∧15\|Air. H = Ta₂O₅, L = SiO₂	−0.04	488.5	Theoretically, not angle tolerant
Plasmonic Filter II [17]	5 layers hybrid plasmonic filter: Substrate\|TiO₂(25.4nm)/ Ag(26.3nm)/TiO₂(43.8nm)/Ag(30nm)/TiO₂(107.7nm)\|Air	−1	488.5	0° - 50°

System Component		Model name	Spectral characteristics
White LED		MCWHL5 – Thorlabs [27]	As shown in Fig. 3.
Blue filters	Dielectric Filter	A 120 layers filter adopted from [4]	As shown in Fig. 4(a).
Blue filters	Plasmonic Filter	A 5 layer filter adopted from [17]	As shown in Fig. 4(a).
Biased- Si PD		DET10A – Thorlabs [28]	As shown in Fig. 3.

	Structure	T_max (dB)	λ_Cut-off (nm)	Angle tolerance
Dielectric Filter I [4]	120 layers all-dielectric filter: Substrate\|1.8 (0.5LH 0.5L) ^∧15 1.5(0.5LH 0.5L) ^∧15 1.2(0.5LH 0.5L) ^∧15 (0.5L H 0.5L) ^∧15\|Air. H = Ta₂O₅, L = SiO₂	−0.04	488.5	Theoretically, not angle tolerant
Plasmonic Filter II [17]	5 layers hybrid plasmonic filter: Substrate\|TiO₂(25.4nm)/ Ag(26.3nm)/TiO₂(43.8nm)/Ag(30nm)/TiO₂(107.7nm)\|Air	−1	488.5	0° - 50°

System Component		Model name	Spectral characteristics
White LED		MCWHL5 – Thorlabs [27]	As shown in Fig. 3.
Blue filters	Dielectric Filter	A 120 layers filter adopted from [4]	As shown in Fig. 4(a).
Blue filters	Plasmonic Filter	A 5 layer filter adopted from [17]	As shown in Fig. 4(a).
Biased- Si PD		DET10A – Thorlabs [28]	As shown in Fig. 3.

Impact of blue filtering on effective modulation bandwidth and wide-angle operation in white LED-based VLC systems

Abstract

1. Introduction

2. Theoretical background and VLC link model

2.1 Phosphor-coated white LED operation

2.2 LED modulation process and link model

2.3 Effective PD responsivity

2.4 Power gain coefficients

3. Blue filtering effect

4. Results and discussion

4.1 Upper and lower bounds of modulation bandwidths

4.2 Wide-angle performance

4.3 Blue filters effect on f_3dB

4.4 Figure of merit (FOM)

4.5 Averaging effect

4.6 Numerical example and OSNR

5. Conclusion

Funding

Acknowledgment

References

Cited By

Figures (13)

Tables (2)

Equations (25)

OSA Continuum

Abstract

1. Introduction

2. Theoretical background and VLC link model

2.1 Phosphor-coated white LED operation

2.2 LED modulation process and link model

2.3 Effective PD responsivity

2.4 Power gain coefficients

3. Blue filtering effect

4. Results and discussion

4.1 Upper and lower bounds of modulation bandwidths

4.2 Wide-angle performance

4.3 Blue filters effect on f3dB

4.4 Figure of merit (FOM)

4.5 Averaging effect

4.6 Numerical example and OSNR

5. Conclusion

Funding

Acknowledgment

References

Cited By

Figures (13)

Tables (2)

Equations (25)

OSA Continuum

4.3 Blue filters effect on f_3dB