Add a gradient of intensiy to an interference plot - r

Question

I want to plot the gradient plot of intensities, something like this:
I though myself about creating a gradient grid whose distribution was my "I" function, but I have no idea how to do it or if there is an explicit package in R to accomplish this task.
Thank you so much for even thinking about this.
a <- 5*10^(-6)
d <- 0.5*0.005
l <- 500*10^(-9)
n <- pi
theta <- seq(-n,n,length=3500)
I <- function(x){(cos((pi*d*sin(x))/l))^2*(sin((pi*a*sin(x))/l)/((pi*a*sin(x))/l))^2}
y1 <- lapply(theta,I)
y <- unlist(y1)
df <- data.frame(theta,y)
I2 <- function(x){(sin((pi*a*sin(x))/l)/((pi*a*sin(x))/l))^2}
y12 <- lapply(theta,I2)
y2 <- unlist(y12)
df2 <- data.frame(theta,y2)
p = ggplot()
p +
geom_line(data = df, aes(theta,y)) +
xlim(-0.3,0.3) +
geom_line(data = df2, aes(theta,y2))

Answer 1

Making use of patchwork this could be achieved like so:
For the gradient make a second ggplot of rectangles using e.g. geom_rect where you map intensity on color and/or fill
This gradient plot could then be glued to the main plot via patchwork
To get a nice gradient plot
I tripled the number of grid points for the gradient plot,
mapped the cubic root of intensity on color and
get rid of all unnecessary elemnts like y-axis, color guide, ...
BTW:
As your functions are vectorized you don't need lapply to compute the intensities.
Instead of adjusting the limits via xlim() (which removes rows falling outside of the range), set them using coord_cartesian.
library(ggplot2)
library(tibble)
library(patchwork)
a <- 5*10^(-6)
d <- 0.5*0.005
l <- 500*10^(-9)
n <- pi
theta <- seq(-n,n,length=3500)
I <- function(x){(cos((pi*d*sin(x))/l))^2*(sin((pi*a*sin(x))/l)/((pi*a*sin(x))/l))^2}
y <- I(theta)
df <- data.frame(theta,y)
I2 <- function(x){(sin((pi*a*sin(x))/l)/((pi*a*sin(x))/l))^2}
y2 <- I2(theta)
df2 <- data.frame(theta,y2)
p1 = ggplot() +
geom_line(data = df, aes(theta,y)) +
geom_line(data = df2, aes(theta,y2)) +
coord_cartesian(xlim = c(-0.3,0.3))
g <- tibble(
xmin = seq(-n, n, length = 3 * 3500),
xmax = dplyr::lead(xmin),
y = I(xmin)
)
p2 <- ggplot(g, aes(xmin = xmin, xmax = xmax, ymin = 0, ymax = 1, color = y^(1/3))) +
geom_rect() +
coord_cartesian(xlim = c(-0.3,0.3)) +
guides(color = FALSE) +
theme_minimal() +
theme(axis.ticks.y = element_blank(), axis.text.y = element_blank())
p1 / p2 + plot_layout(heights = c(10, 1))
#> Warning: Removed 1 rows containing missing values (geom_rect).