The script language OptiGrating 4.2 uses is a programming language based on the

BASIC language syntax. You use the script language to define the shape, chirp, and

apodization of a grating. To enter this definition, you have to choose the User Defined

option.

## Variables, Arrays, and Operators

**Variables**

A variable name can be any string beginning with a character. You cannot use special

characters and operators in the name. Some names are reserved for commands,

predefined constants, and functions. Variable names are case sensitive. For

example, ‘**a**’ is not the same as ‘**A**’; ‘**Pos**’ is not the same as ‘**pos**’ or ‘**POS**’.

Examples:

Valid variable names: **a, pos, lambda, width1**

Invalid variable names: ***a, _pi, IF, RETURN**

**Note**: Comment lines in the editing area are preceded by the double slash symbol //.

**Arrays**

You can use only one-dimensional arrays. You do not have to declare an array before

using it. For the array index, you can use a positive or a negative integer. The usage

format is** array_name[index].**

Examples:

**A[2]**

**B[-3]**

**a[x]=x*2**

**Mathematical Operators**

OptiGrating supports the following standard mathematical operators. (listed in

decreasing priority):

**^ power * multiplication / division + addition – subtraction**

**Boolean Operators**

OptiGrating supports the following standard Boolean operators.

**= equal to < less than > more than & and | or Examples: A=b A<b B&c C|d**

**Comparison Operators**

The Comparison operators can be combined:

**a<=b; a<>b; a=>b**

## Commands and Statements: RETURN, IF, ERROR

All command and statement names must be in upper case letters.

Examples:

**IF is a command If or if can be a variable**

The script language has a set of commands and control statements. However, not all

of them are needed to define user shape, chirp, and apodization. Therefore, here is a

list of the commands useful in OptiGrating.

**The RETURN Command**

The RETURN keyword terminates execution of the program in which it appears and

returns the control (and the value of expression, if given). Notice that if you don’t

specify RETURN in your program, the interpreter will return the value of expression

in the last logical order. You usually use the RETURN command if your program uses

IF – THEN commands.

Syntax: RETURN[expression]

Example 1:

A program with only one line (you don’t have to specify RETURN)

**sin(3)*24+13*(2+6)**

returns 107.38688. The same result is obtained from the program:

**RETURN sin(3)*24+13*(2+6)**

Example 2:

Consider the program:

**cp = 100 a = Length-x IF x<cp THEN RETURN x ELSE RETURN a**

The above program returns x if x is less than 100. Otherwise, it returns Length-x if x

is larger or equal than 100.

Example 3:

Let’s modify the previous example, Example 2, as follows:

**cp = 100 a = Length-x IF x<cp THEN b = x ELSE b = a RETURN b**

This example gives the same result as Example 2. The difference is that another

variable b is used instead of returning the value of a directly.

**The IF Statement**

The IF statement controls conditional branching. The body of an IF statement is

executed if the value of the expression is nonzero. The syntax for the IF statement

has two forms.

Syntax1: IF expression THEN statement

Syntax2: IF expression THEN statement ELSE statement

In both forms of the IF statement, the expressions, which can have any value, are

evaluated, including all side effects.

In the first form of the syntax, if expression is nonzero (true), the statement is

executed. If expression is false, statement is ignored. In the second form of syntax,

which uses ELSE, the second statement is executed if expression is false. With both

forms, control then passes from the IF statement to the next statement in the program.

Examples:

The following are examples of the IF statement:

**IF i > 0 THEN y = x / i ELSE x = i**

In this example, the statement y = x/i is executed if i is greater than 0. If i is less than

or equal to 0, i is assigned to x.

For nesting IF statements and ELSE clauses, use BEGIN – END to group the

statements and clauses into compound statements that clarify your intent. If no

BEGIN – END are present, the interpreter resolves ambiguities by associating each

ELSE with the closest IF that lacks an ELSE.

**IF i > 0 THEN // Without BEGIN – END IF j > i THEN x = j ELSE x = i**

The ELSE clause is associated with the inner IF statement in this example. If i is less

than or equal to 0, no value is assigned to x.

**IF i > 0 THEN BEGIN /* With BEGIN – END */ IF j > i THEN x = j END ELSE x = i**

The BEGIN – END enclosing the inner IF statement in this example makes the ELSE

clause part of the outer IF statement. If i is less than or equal to 0, i is assigned to x.

**The ERROR Keyword**

The ERROR keyword stands for a constant and returns the error code (if any). In case

of a mathematical error, like division by zero or overflow, it will reset the error flag.

The constant returns the error code (if any) and in cases of mathematical errors

(division by zero, overflow, etc.) resets the error flag. This allows you to detect any

unexpected errors during calculation. The best example is to use the ERROR

command in the IF-THEN-ELSE statement.

Example 1:

The following one-line program

**Length /x**

results in the Error message: Division by zero, b=Length/x?????

This occurs because initially x has been set to 0.

Example 2:

Consider the program:

**b=Length/x IF ERROR THEN b=100; RETURN b**

Now, whenever we have a mathematical error, b is set to 100 and the program will

continue without the error message.

ERROR is a constant, and you cannot assign any other value to it.

**The FIRSTTIME Keyword**

Flag – indicates FIRST time internal run.

Example:

**S =7 IF FIRSTTIME THEN RETURN 100 RETURN x*s**

## Input dialog box

This dialog will appear if you use INPUT or GINPUT in User Defined Functions.

Syntax:

**INPUT variable INPUT “string” variable INPUT “string” variable = init value GINPUT variable=init value GINPUT “string” variable = init value**

**Example INPUT**

Usage of INPUT is limited. Because in OptiGrating you use user defined functions

usually in a loop, INPUT will ask you to input data every time you repeat the loop

(usually more than 100 times). To avoid this and to avoid redundant programming (IF

FIRSTTIME THEN …), use the function GINPUT (general input), which will ask you

for input data only the first time you enter the loop.

**INPUT** variable

**INPUT** “string” variable

**INPUT** “string” variable = init value

Example:

**b=1 MAX = 8 INPUT “Factorial of:” MAX**

……

You will get the same effect if you use:

**b=1 INPUT “Factorial of:” MAX = 8**

You will be asked to type a value in the Factorial Of box in the Input window.

**Note**: The initialization of MAX before INPUT is not necessary. If you delete the

line MAX = 8, the default value in the Input box will be 0.

**Example GINPUT**

**GINPUT** variable=init value

**GINPUT** “string” variable = init value

(general input)

Displays an Input window on the screen. (The text is optional.)

If the whole program (User Defined Function) is running more than once in the logical

(internal) block, GINPUT will ask you to enter data only the first time the program runs.

Example:

In OptiGrating, you will use the Apodization function :

**s=4 tanh(s*(x/Length))*(tanh (s*(1-x/Length)))**

Because each grating length is divided into a number of steps (let’s say 25), this

function will be called more than once per grating (25 times).

**Note**: Variable x will vary in each step: x(actual) = x(previous) + Length/25

In the Apodization function, you have one parameter “s” for changing the shape of the

apodization function. If you want to test different shapes, you will need to change the

value for each calculation. Instead of going through all dialog boxes and buttons to

reach the User Function dialog box, whenever you want to change “s”, you can use

the **GINPUT** function:

**GINPUT “Input Shape parameter” s=4 tanh(s*(x/Length))*(tanh (s*(1-x/Length)))**

You will be asked to input different “s” values each time you press the Calculation

button. Thus, you will be able to try different apodization shapes very quickly and

easily.

## Constants

**Mathematical Constants**

pi 3.14159265358979323846

e 2.71828182845904523536

**Physical Constants**

_c | - 9979e8
| m/s | Speedoflightinfreespace |

_e | - 8542e-12
| F/m | Permittivityinfreespace |

_mi | 4*pi*10e-7 | H/m | Permeabilityinfreespace |

_q | - 60219e-19
| C | Elementarycharge |

_me | - 1095e-31
| kg | Freeelectronmass |

_u | - 660531e-27
| kg | Atomicmassunit |

_mp | - 672614e-27
| kg | Protonrestmass |

_mn | - 674920e-27
| kg | Neutronrestmass |

_eV | - 60219e-19
| J | Energyunit(electron-volt) |

_h | - 626e-34
| Js | Planckconstant |

_hr | - 05459e-34
| Js | ReducedPlanckConstant |

_lc | - 4263096e-12
| m | Comptonwavelengthofelectron |

_Ry | 13.6058 | eV | Rybergenergy |

_ri | - 09737312e7
| 1/m | Rydbergconstant |

_kT | 25.853 | meV | Thermalenergy |

_NA | - 022045e23
| Avogadronumber | |

_f | - 6486e4
| C/mol | Faradayconstant |

_a | - 297351e-3
| Fine | structureconstant |

_a0 | - 2917715e-11
| m | Bohrradius |

_re | - 817939e-15
| m | Electronradius |

_mb | - 274096e-24
| J/T | Bohrmagnetron |

_kB | - 3807e-23
| J/K | Boltzmannconstant |

_sb | - 66961e-8
| Stefan-Boltzmannconstant |

## Functions

**Commonly Used Functions**

sin(radian) | sine |

asin({0..1) | radian |

sinh(x) | hyperbolic sine of x |

cos(radian) | {0..1} |

acos({0..1}) | radian |

cosh(x) | hyperbolic cosine of x |

tan(radian) | {0..inf} |

atan({0..1}) | radian |

exp(x) | e^x |

ln(x) | log in base e |

log(x) | log in base 10 |

deg(rad) | radians into degrees |

rad(deg) | degrees into radians |

fact(x) | x factorial (x!) |

sqrt(x) | square root of x |

pow(x,n) | x^n |

**Other Functions**

min(a,b) =a if a<b else b

max(a,b) =a if a>b else b

comb(n, k)= number of combinations for k object , n – return 0 total number of objects (n>=m),

if error

perm(m, n) =permutation mPn (0 if error)

gcd(a, b) = Greatest Common Divisor between a & b

lcm(a, b) = Largest Common Multiple between a & b

frc(x) = fractional part of ‘x’

int(x) = integer part of ‘x’

a>n0g alen(dx,y) Computes angle from Cartesian position (x,y), angle defined positive if y

negative if y < 0

randrand(MaxNum) => Randomize {0..MaxNum}

**Fresnel Integral**

fresnel_s(x) = Fresnel Integral SIN

fresnel_c(x) = Fresnel Integral COS

Evaluates the Fresnel integrals

fresnel_ffresnel_f(x) = function f(x) related to the Fresnel Integral

fresnel_g(x) = function g(x) related to the Fresnel Integral

Evaluates the functions f(x) and g(x) related to the Fresnel integrals by means of the

formulae

**Gamma Functions**

Computes the value of the gamma function at x

gamma(x)Gamma Function

lgamma(x)Natural logarithm of Gamma Function, x – must be positive

**Error Function**

erf(x)Error Function

erfc(x) Complementary Error Function”},

Computes the error function erf(x) and Complementary error function erfc(x)

When x>26 then erf(x)=1 and erfc(x)=0

When x< -5.5 then erf(x)=-1 and erfc(x)=2;

nexperfcNon exp erfc computes exp(x^{2})^{∗}erfc(x)

Inverse error function y(x)

inverf(x,minx)

Evaluates the inverse error function y(x) where

x – it is necessary that -1 <x < 1

if |x| > 0.8 then value of x is not used in the procedure

minx if |x| <= 0.8 then value minx is not used in the procedure

if |x|> 0.8 then minx has to contain the value of 1-|x|.

In the case that |x| is in the neighborhood of 1, cancellation of digits take place in the

calculation of 1-|x|

If the value 1-|x| is known exactly from another source, then minx has to contain this

value, which will give better results.

## Bessel Functions

**Bessel function J**

bessj0(x) – Bessel function J0(x) of the 1st kind of order 0

bessj1(x) – Bessel function J1(x) of the 1st kind of order 1

bessj [k] (x) – Bessel function Jk(x) of the 1st kind in order k

**Bessel function Y (Weber’s function )**

bessy0(x) – Bessel function Y0(x) of the 2nd kind of order 0

bessy0(x) – Bessel function Y1(x) of the 2nd kind of order 1

bessy [k] (x) – Bessel function Yk(x) of the 2nd kind of order k

**Modified Bessel function I**

bessi0(x) – Modified Bessel function I0(x) of the 1st kind of order 0

bessi1(x) – Modified Bessel function I1(x) of the 1st kind of order 1

bessi [k] (x) – Modified Bessel function Ik(x) of the 1st kind of order k

**Modified Bessel function K**

bessk1(x) – Mod. Bessel function K0(x) of the third kind of order 0

bessk1(x) – Mod. Bessel function K1(x) of the third kind of order 1

bessk [k] (x) – Mod. Bessel function Kk(x) of the third kind of order k

**Spherical Bessel functions**

spbessj[k](x) => Spherical Bessel funct. Jk+0.5(x)

Bessel function of the second kind (Neumann’s functions)

neumann(a,x) – Neumann function Ya(x) of the 2nd kind of order a

neumann1(a,x) – Neumann function Ya+1(x) of the 2nd kind of order a

**Chebyshev Polynomials**

chepol(n,x) – Computes the value of the Chebyshev polynomial Tn(x)

## Conversions

**Length**

ft_m | ft_m(foot) | Foottometer |

yd_m | yd_m(yard) | Yardtometer |

in_m | in_m(inch) | Inchestometer |

**Temperature**

c_k | c_k(celsius) | Celsius to Kelvin |

fh_k | fh_k(farenheit) | Farenheit to Kelvin |

fh_c | fh_c(farenheit) | Farenheit to Celsius |

k_c | k_c(kelvin) | Kelvin to Celsius |

c_fh | c_fh(celsius) | Celsius to Farenheit |

k_fh | k_fh(kelvin) | Kelvin to Farenheit |

**Other Conversions**

gal_l | gal_l(gallon) | Gallontoliter |

pt_l | pt_l(pint) | Pinttoliter |

oz_l | oz_l(oz) | Oztoliter |

in3_l | in3_l(cubInc) | CubicInchtoliter |

l_m3 | l_m3(liter) | Literto cubicmeter |

pd_kg | pd_kg(pound) | Poundtokilogram |

phe | phe(wavelength[µm]) | CalculatePhotonenergy[eV] |